  This paper studies a slow-fast system whose principal characteristic is that
the slow manifold is given by the critical set of the cusp catastrophe. Our
analysis consists of two main parts: first, we recall a formal normal form
suitable for systems as the one studied here; afterwards, taking advantage of
this normal form, we investigate the transition near the cusp singularity by
means of the blow up technique. Our contribution relies heavily in the usage of
normal form theory, allowing us to refine previous results.
