The best theory about who killed Anastasia was that it was a conspiracy led by Joe Biondo. Under Mangano, Biondo was the consigliere but was demoted to captain by Anastasia. Steve Armone was part of his group. Jerry Capeci covered this in more detail. There's no proof that Genovese had anything to do with it.

Genovese gets credit for more than he did. He was said to have hired Carmine Galante to kill Carlo Tresca in 1943. The major problem here is that Genovese and Galante were in different borgatas, and Tresca was known to have gone after Frank Garofalo in his newspaper. It's clear that the order came from Joe Bonanno or Frank Garofalo. Genovese had nothing to do with it.

As for who set up Genovese against Costello, it was discovered that Tony Bender was giving both Genovese and Costello information against each other, so Genovese was led to believe that Costello was going after him. Costello and Genovese reconciled in prison and the order was given to make Bender "disappear;" and regarding Genovese going to prison for narcotics trafficking, Tom Tripodi of the Bureau of Narcotics wrote that he helped in "setting him up."

A known dealer was recognized by Genovese. He said "Hi" or something to him, and that act of recognition was used against him to put him away. Other Mob members who were around during that time period and knew him denied that Genovese was a drug trafficker. No doubt he took a cut from the proceeds from members of his crime family who were traffickers, but probably gave lip service to the order to lay off drugs of face the death penalty. It seems what they did instead was to cut off all aid to their members who were arrested for drugs.

Vito Genovese's time as boss of the former Costello crime family lasted for eleven years, but almost ten of those were in prison in Atlanta. For most of the time Genovese was boss, his crime family was run by his underboss, Gerry Catena. For all the claims about Genovese being a "boss of bosses" or the most powerful boss on the Commission, the evidence shows that simply wasn't true. In fact, the whole claim that one boss gave orders to the others is bogus. All of the New York bosses were equal, except for Joe Bonanno who essentially lost his Family and was in a war from 1964 to 1968. Carlo Gambino didn't move up to become boss of bosses after Genovese went to prison or died: there was no boss of bosses, not since 1931.