  In order to describe the asymptotic behaviour of a vanishing period in a one
parameter family we introduce and use a very simple algebraic structure :
regular geometric (a,b)-modules generated (as left $\A-$modules) by one
element. The idea is to use not the full Brieskorn module associated to the
Gauss-Manin connection but a minimal (regular) differential equation satisfied
by the period integral we are interested in. We show that the Bernstein
polynomial associated is quite simple to compute for such (a,b)-modules and
give a precise description of the exponents which appears in the asymptotic
expansion which avoids integral shifts. We show a couple of explicit
computations in some classical (but not so easy) examples.
