I never bought the whole “Gotti killed Desimone” thing, that was just a myth. True he wasn’t an made guy or anything more of a nuisance but I do think it’s possible that the Gambinos and Luccheses discussed this since he did murder two Gambinos associates but yeah I agree the Luccheses dealt with it internally like in the movie
Thats probably the best answer Crusher and very likely what happened. Because he was close to Jimmy Burke and with the Vario crew, Gotti requested DeSimone's head to which Vario probably said "no problem but we willl take care of it". Im sure Vario didn't love the fact that he had to clip DeSimone but he understood why he had to go for a variety of reasons.
