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