Coeffective and de Rham cohomologies on almost contact manifolds

We discuss the relation of the coeffective cohomology of some classes of almost contact manifolds with the topology of the manifold. A topological bound for the coeffective numbers is obtained. The lower bound is attained for compact cosymplectic manifolds, and the upper one for contact and (non-compact) exact almost cosymplectic manifolds. Finally, the behaviour of the coeffective cohomology under deformations is studied and an almost cosymplectic version of the Moser Stability Theorem is given.