Let $M$ be a connected closed orientable manifold with Euler characteristic $0$. Let $TM$ be the tangent bundle over $M$ and $SM$ be the induced sphere bundle with fiber $S^{n-1}$.
Looking at page 432 of Hatcher's book "Algebraic Topology", I'm trying to see if the fiber bundle $SM$ satisfies all the requirements of the Leray-Hirsch theorem, with coefficient ring $\mathbb{Z}$.
I can verify that condition $(a)$ is satisfied, the cohomology groups of the sphere are always finitely generated for every dimension. I'm stumped for condition $(b)$. To be honest I'm not sure I understand its statement at all.
Could I get an explanation about what that condition is saying, so that I can attempt to verify for $SM$?