  We investigate the classical and quantum behavior of a Bianchi I model in the
presence of a stiff matter contribution when the Vilenkin interpretation of the
wave function of the Universe is taken into account. We study its evolution in
the so-called polymer representation of quantum mechanics, in order to
characterize the modifications that a discrete nature in the isotropic variable
of the Universe induces on the morphology of the cosmological singularity. We
demonstrate that in such a model the Big-Bang singularity is removed at a
semiclassical level in favor of a Big-Bounce when a lattice on the isotropic
variable is considered. Furthermore, the analysis of the mean values on the
quantum degrees of freedom, \textit{i.e} the variables $\beta_{+},\beta_{-}$ in
the Misner picture, and the investigation on the evolution of the wave packets
show how the typical diverging behavior associated to the anisotropies of the
Universe in proximity of the initial singularity disappears in our polymer
modified scheme. Indeed, the anisotropies remain finite across the Big-Bounce
and they assume a value that depends on the initial conditions fixed far from
the turning point. Finally, we demonstrate that the proposed scenario can be
extended, with a suitable choice of the configuration parameters, to the
Bianchi IX cosmology and therefore it can be regarded as a paradigm for the
generic cosmological model.
