The Rizzutos cut ties with the Bonanno family when they found out that Joe Massino ordered Gerlando Sciascia killed. Sciascia was related to the Rizzutos from Sicily. Peter Edwards is not wrong in saying that Rizzuto cut ties with the Bonanno, but he is only going the Sicilian line, not the Calabrians. The ties remained with the old Cotroni family.
Salvatore Montagna began betraying members of his own circle. This is what led to his down fall and fracturing those against the Rizzutos. There were Bonanno capos in New York that did not like Sal cause he was picked to be a capo by a rat. Once he became acting boss as Massino no longer had the power to appoint members in the family, many of his detectors held their tongues. Mancuso stole the family from Basciano, which the two factions were rivals. Montagna was Mancuso pick. Best if Mancuso stayed in New York, cause both Sicilians and Calabrians in Montreal would more likely shoot him on sight boss or no boss.
Buffalo comes up a lot. To understand that connection Buffalo Violi, Hamilton Joe Violi to be precise was sending cash and weapons to his Violi cousins who are part of the Cotroni family of Montreal. Nicolo Rizzuto, Paolo Renda, and Agostino Caruana, were mostly likely done by the Violi in Montreal, and has since then remained quiet, so they participated at the start of the war at least. Of the big four Domenico Manna is still alive.
Rizzuto meeting with Bonanno representatives after his release from prison has been documented by an informant, and wire taps on high level members in the Toronto area. Not long after that is when Rizzuto rivals began to fall. So there is some weight that Montagna was backed by the Bonanno crime family and Rizzuto was able to make them stay out of the conflict.
With the Violi locked up, that leaves the Luppinos on the streets and only targets available.