At least before he went to jail, Gerry Catena was the highest ranking member of the family on the streets, Vito made him acting boss. Tommy Eboli was second in command and the day to day boss on the NY side of the Hudson. Mike Miranda was the consigliere, and until Catena went to jail on contempt charges those three were meeting on important family matters, with Catena having the final say. This was indicated by the Mary Ferrell FBI docs, which had transcripts of Eboli talking with various people, including his brother, Vito's brother and Benny Squint himself, and the Jersey Mafia book, which had the transcripts from the Barn where Ray DeCarlo met with a ton of different people.

After Catena got out of jail is when things get murky. Apparently he never wanted to be boss, but only took the job out of obligation. He was one of if not the wealthiest mobsters in the country, and Vito was dead, so when he got out of jail he immediately retired to Florida. Supposedly he and Carlo Gambino pushed for Tieri to be boss, while some say that the rest of the family wanted Lombardo.

I personally believe that Tieri was at least for some time in the 70's the actual boss, but he was really sick so it would not surprise me if at some point he was replaced by Gigante or Salerno, who at time were in better health. My question is, why would Tieri, who was mega rich and not in good health, and later Salerno, who was maybe even wealthier and also sick, subject themselves to the stress of the boss job on a daily basis only to let Lombardo and then the Chin swoop in to have the final say on the really important matters? Was there some type of financial incentive? You would think that being the front boss would not be worth the headaches.