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When we consider a proper holomorphic map \ $\tilde{f}: X \to C$ \ of acomplex manifold \ $X$ \ on a smooth complex curve \ $C$ \ with a criticalvalue at a point \ $0$ \ in \ $C$, the choice of a local coordinate near thispoint allows to dispose of an holomorphic function \ $f$. Then we mayconstruct, using this function, an (a,b)-modules structure on the cohomologysheaves of the formal completion (in \ $f$) \ of the complex of sheaves \$(Ker\, df^{\bullet},d^{\bullet})$. These (a,b)-modules represent a filteredversion of the Gauss-Manin connection of \ $f$. The most simple example of thisconstruction is the Brieskorn module (see [Br.70]) of a function with anisolated singular point. See [B.08] for the case of a 1-dimensional criticallocus. But it is clear that this construction depends seriously on the choiceof the function \ $f$ \ that is to say on the choice of the local coordinatenear the critical point \ $0$ \ in the complex curve \ $C$. The aim of thepresent paper is to study the behaviour of such constructions when we make achange of local coordinate near the origin. We consider the case of \$[\lambda]-$primitive frescos, which are monogenic geometric (a,b)-modulescorresponding to a minimal filtered differential equation associated to arelative de Rham cohomology class on \ $X$ \ (see [B.09-a] and [B.09-b]). Anholomorphic parameter is a function on the set of isomorphism classes offrescos which behave holomorphically in an holomorphic family of frescos. Ingeneral, an holomorphic parameter is not invariant by a change of variable, butwe prove a theorem of stability of holomorphic families of frescos by a changeof variable and it implies that an holomorphic parameter gives again anholomorphic parameter by a change of variable. We construct here two differentkinds of holomorphic parameters which are (quasi-)invariant by change ofvariable. The first kind is associated to Jordan blocks of the monodromy withsize at least two. The second kind is associated to the semi-simple part of themonodromy and look like some "cross ratio" of eigenvectors. They allow, in thesituation describe above, to associate to a given (vanishing) relative de Rhamcohomology class some numbers, which will depend holomorphically of our data,and are independant of the choice of the local coordinate near \ $0$ \ to studythe Gauss-Manin connection of this degeneration of compact complex manifolds.

Contruction of holomorphic parameters invariant by change of variable in the Gauss-Manin connection of an holomorphic map to a disc