  In this paper we consider holomorphic families of frescos (i.e. filtered
differential equations with a regular singularity) and we construct a locally
versal holomorphic family for every fixed Bernstein polynomial. We construct
also several holomorphic parameters (a holomorphic parameter is a function
defined on a set of isomorphism classes of frescos) which are quasi-invariant
by changes of variable. This is motivated by the fact that a fresco is
associated to a relative de Rham cohomology class on a one parameter
degeneration of compact complex manifolds, up to a change of variable in the
parameter. Then the value of a quasi-invariant holomorphic parameter on such
data produces a holomorphic (quasi-)invariant of such a situation.
