  We study quantum mechanical systems with a discrete spectrum. We show that
the asymptotic series associated to certain paths of steepest-descent
(Lefschetz thimbles) are Borel resummable to the full result. Using a
geometrical approach based on the Picard-Lefschetz theory we characterize the
conditions under which perturbative expansions lead to exact results. Even when
such conditions are not met, we explain how to define a different perturbative
expansion that reproduces the full answer without the need of transseries, i.e.
non-perturbative effects, such as real (or complex) instantons. Applications to
several quantum mechanical systems are presented.
