I don't think nino liked or respected gotti. gaggi was firmly in the Castellano wing and gotti in the "other" faction with Neil.
He was the only capo not present at the dinner meetings where gotti announced they were investigating pauls murder and then when Decicco proposed gotti as boss. Ive read several times where he wouldn't go meet with gotti and I think it may have been in underboss?? that gotti was getting annoyed by gaggi not fronting.
Whatever the case, Castellano was clipped in Dec 85, Gotti got uped in Jan 86 and Gaggi was convicted and jailed in April 86 so he was only on the street for a couple of months with JG as boss.
The mere and simple fact that Gotti couldn't call Nino in to a meeting speaks volumes. Technically that made them enemies, but Gotti couldn't reach Nino to enforce rules of conduct befitting a Caporegime.
