In this talk we study handle decompositions of 3-manifolds in relation with an invariant defined by Eiji Ogasa. This invariant takes into account the complexity of regular level surfaces of the handle decompositions. We will discuss the relationship of the Ogasa invariant with the topology of the 3-manifold. Comparison with the Heegaard genus will give some informations about the geometry of the 3-manifold.
This is a joint work with Gioia Vago.