  We outline the covariant nature,with respect to the choice of a reference
frame, of the chaos characterizing the generic cosmological solution near the
initial singularity, i.e. the so-called inhomogeneous Mixmaster model. Our
analysis is based on a "gauge" independent ADM-reduction of the dynamics to the
physical degrees of freedom. The out coming picture shows how the inhomogeneous
Mixmaster model is isomorphic point by point in space to a billiard on a
Lobachevsky plane. Indeed, the existence of an asymptotic (energy-like)
constant of the motion allows to construct the Jacobi metric associated to the
geodesic flow and to calculate a non-zero Lyapunov exponent in each space
point. The chaos covariance emerges from the independence of our scheme with
respect to the form of the lapse function and the shift vector; the origin of
this result relies on the dynamical decoupling of the space-points which takes
place near the singularity, due to the asymptotic approach of the potential
term to infinite walls. At the ground of the obtained dynamical scheme is the
choice of Misner-Chitre' like variables which allows to fix the billiard
potential walls.
