On the Variations of the Betti Numbers of Regular Levels of Morse Flows

We generalize results in [C-dR] by completely describing how the Betti numbers of the boundary of an orientable manifold vary after attaching a handle, when the homology coefficients are in Z, Q, R or Z/pZ with p prime. Next we consider the Ogasa invariant associated with handle decompositions of manifolds. We make use of the above results in order to obtain upper bounds for the Ogasa invariant of product manifolds.