Great analysis Lana Bada bing! with the unknown traitor who actually killed Michael still in the family loose even more chaos” and "bloodshed"
He was slippin' inserting himself in a turf war backing up the Rosatos against Pentangeli the Corleone caporegime, Pentangeli as the fall guy, was his failure

I reckon this fixation in framing Pentangeli is what handed Michael the decisive victory and he was comprehensively beaten
He could have outsmarted Michael but let him outsmart him by overplaying his hand

If there was no "New York connection." I reckon Michael would have been pretty much clueless trying to figure out who was behind the Tahoe shooting

You are right Woltz, Michael was not expecting “push back” from Roth, who had just gifted their hotel! he probably would not have been, even in the frame and could have continued flying under the radar

I reckon, each of them knew or almost knew, what the other was up to, by that time of their meeting at Roth's house but "This is the business we've chosen" scene in Roth's hotel suite in Havana no doubt confirmed it

They hung on: Michael wanting to learn who was the traitor in his family and Roth for Michael to be taken home in a military car -- alone-- for his protection