The sequence in the novel always bothered me a little because it seems that by getting rid of Moe before they made the move against Barzini and Tattaglia , the Corleones might be showing their hand a little bit.
I mean if I were Barzini and I'm pushing around the Corleones, taking over their gambling and loan sharking rackets, chasing them off the docks and maybe starting to cut them out of their narcotics payoffs and they do nothing, then I will think they are soft and weak. But if I hear that some new Corleone hitman who no one's heard of before takes out Moe Green, then maybe I should reassess, no?
Moe was small potatoes. Had Barzini's attempt to kill Michael and become the big cheese been successful, he would have never kept his end of the deal with Moe Green.
So Barzini may have not viewed Michael's move against him as any kind of threat to him. In fact Barzini probably figured,
"good, Michael Corleone has done my dirtywork for me." Barzini's thinking was probably that since Michael moved Moe out, now all he had to do was take Michael out and he'd automatically be the Capo Di Tutti Capi and the casino that Michael had taken from Moe would become his (Barzini's) without his having to take out Moe Green himself. His thinking probably was that
"The Corleone's have given me one less thing to worry about by killing Moe Green."Remember that at that point, in Barzini's mind, the Corleone's were powerless. At that point, Barzini had already began seeing himself sitting on the throne.
