Sammy actually became close with Frank DeCicco when his mentor, Toddo Aurello died and DeCicco took over Aurello's crew.
There were several incidents which took place over time that made Gravano turn on Castellano. One of them being that Sammy found out that Castellano had secretly ordered Frank DeCicco to kill him, Gravano, had he he opposed an ordered hit that had been taken out on his brother-in-law Nicky Scibetta.
After another incident Gravano learned that once again, for a second time, Big Paul was considering having him killed. And when Gravano began earning more and more from his businesses, Big Paul began to squeeze every last nickel out of him.
Meanwhile the Dellacroce crew were being treated like the red headed stepchildren of the gambino family. But in my opinion, the straw that broke the camel's back in pushing Gotti over the edge with Castellano was Casteallano's failure to both visit Mr. Neil, when he ws dying, or attend his funeral when he did die.
So now you had two factions of the Gambino family who were not happy with the boss, Big Paul. Throw in the fact that Big Paul was probably going to be put away, and that he would in all likelyhood pass over Frank DeCiccio in naming him acting boss had he been sent to prison...and you have all the ingredients to unite two crews to conspire to overthrow the head of the family.
It was really Robert 'DB' DeBernardo who brought Gotti, DeCicco and The Bull together to unite against Paul Castellano.