Bonanno's discussion of the "liberal faction" is interesting, in that he notes that, prior to the ouster of Costello and murder of Anastasia, this was not a strictly unified bloc. Rather, Bonanno defined this tendency as one based on cultural dynamics as much as, if not more than, political unity:
Indeed, Bonanno goes on to characterize the murder of Anastasia (which, of course, took place while Bonanno was off in Palermo) and the subsequent Commission meeting (an emergency meeting, not on the prescripted 5-year schedule), as constituting a "coup for the liberal wing". While Bonanno obviously claimed Anastasia for the "Americanized" group, he also highlighted the tensions among the bosses in this tendency and even claimed that Anastasia came to him to seek Conservative approval of a hit on Genovese after the attempt on Costello (which Bonanno, forever the Dove of Peace, declined to sanction).If the Commission had its conservative, or Sicilian, wing, it also had its liberal, or American, wing. As a general rule, although they didn't always side together, men such as Luciano, Lucchese, Genovese, Anastasia, and Gambino represented new tendencies in our Tradition. All of these men, to a greater or lesser extent, reflected and embodied American trends which we of the old school found distasteful and potentially ruinous.
Bonanno declines to name the principal agents behind Anastasia's murder, noting that the men immediately responsible for the murder were in Anastasia's Family and this was thus an internal concern; he was interested only in the broader political ramifications (Bonanno, always preoccupied with loftier matters lol). Bill Bonanno, however, in "The Last Testament..." does outright claim that Lucchese and Genovese were the prime movers of the Anastasia hit, which allowed them to cement their control of the "liberal wing" by installing their man Gambino. Bill doesn't paint Gambino as a puppet, though he does call him "somewhat servile", overall painting him as a man with more "brains" than "guts". Bill also states that Gambino's installation was approved by Joe Bonanno, to prevent further bloodshed and instability (something that, IIRC, Bonanno himself did not state). Bill claims that Gambino was installed on an interim, probationary basis in 1957, to last three years (that Gambino was indeed on a probationary mandate at this time was also confirmed by an FBI Chicago bug of a conversation between Accardo and Giancana). Interestingly, Bill also claims that during this probationary period, the Gambinos were under something like a receivership status, with Gambino reporting to Lucchese as if the latter were his Avugad for the three-year probation.
Regarding Anastasia, Bill also had an interesting story for the 1956 Commission meeting. Accardo was stepping down and thus Giancana was formally introduced to the Commission in '56 as Chicago's new rappresentante/avvocato. Bill was present at this meeting as an aide to his father and claimed that immediately upon the opening of the meeting, Giancana caused a major uproar by baiting Anastasia in front of everyone, demanding of Anastasia how he planned to kill Frank Scalise. According to Bill, Joe Bonanno had to physically separate the two and it left a major shadow over the already tense political state of the time, highlighting the strengthening undercurrents of factionalism. Bill notes that if Costello were first forced out, Giancana "would risk few repercussions" for his "outrageous affront" to Anastasia's honor and sovereignty as rappresentante "if Anastasia were to have an unfortunate accident".
Now, it's clearly not a side point that the '56 meeting was quite literally opened by Chicago's new avvocato, who had been Chicago's sotto capo, gravely insulting Anastasia, but the reasons and context for this verbal assault are murky. Bill had previously noted that Chicago typically stayed aloof from close involvement in the fractious politics of the NYC Families, preferring to "sit the fence" and then use their vote to endorse the majority opinion. Indeed, Bill notes that Accardo had specifically abstained from attending the emergency 1953 meeting following Mangano's death for these reasons, so it's surprising that all of a sudden, Chicago had some reason to engage in such overtly hostile engagement with the internal politics of the Anastasia Family.
My guess is that this was a strategic provocation done on behalf of Lucchese and Genovese (who were, I believe, particularly close to Chicago's bosses), to test the waters and ratchet up tensions around Anastasia. It seems evident that Bill was hinting that he also understood Giancana's insult to be linked to the subsequent moves against Costello and Anastasia. Giancana's attack would have, presumably, put significant pressure on Anastasia to save face, and I would suspect spurred Anastasia's decision to actually kill Scalise. Scalise's murder, in turn, was likely the final -- or at least one of the major -- precipitating factors leading to men within Anastasia's Family deciding to kill him, paving the way for Lucchese-Genovese ally Gambino to be put in as boss.
Likely, Anastasia's tenure as boss was something of a lightning rod for broader political tensions in the national organization, along with internal tensions within his own Family. Anastasia rises to power with the murder of Mangano, whom Bonanno cited as one of the "conservatives" aligned with him and Profaci. We know now also that in 1956, Anastasia (likely with the counsel of Costello as well) was taking a central role in enhancing the political status of international Calabrian networks vis-a-vis Cosa Nostra by pushing for the institution of leading 'ndranghetisti as heads of new CN Families in Calabria (something which I believe was also closely connected to the formation of the Ontario crimine, which paved the way also for 'ndrangheta 'ndrine and/or locali to be set up in a number of US cities in the coming years). Anastasia is then put in the position where he likely felt that he had to kill Scalise, which presumably signed his own death sentence. Joe Bonanno was correct, I'm sure, that the immediate agents responsible for his murder were an internal matter, but clearly the events and tensions leading up to it had a much broader scope, of which we only know bits and pieces.