This is what I believe happened during the Mob war in the Novel.

A bomb had exploded in the mall which was thrown from a car that sped off. I believe the Tattaglias did this trying to avenge for what happened to their son, Bruno.

In the downtown area, 2 Corleone Button Men were killed when they were in Greenrich village. My guess is that this was an attack from the Barzinis.

Later on, in the Novel, The Barzini and Tattaglia Families were smashing through the Corleone Family territories: Bookmaking, Garment Center, Union locals, and policy bankers. They even killed a few officials who ran some of those businesses as well as kicking them away. (This was when Sonny was still the acting boss while the Don was still slowly recovering)

When the Corleones first retaliate it says that they killed someone so important that they wish to hide his body. My question would be who do ya think is so important??

When the Corleones retaliate again they massacred Dock goons (Which is owned by the Tattaglias). They killed Tattaglia Family Pimps. And when the Bookmakers were still kicked oiff their property Clemenza's regime was sent to wreak havoc on the shore. My guess is that these were Barzini's people who were invading the businesses over there since it was one of his ambitions to take over part of the Corleone gambling operations