  We analyse the classical and quantum dynamics of a Bianchi I model in the
presence of a small negative cosmological constant characterizing its evolution
in term of the dust-time dualism. We demonstrate that in a canonical metric
approach, the cosmological singularity is removed in correspondence to a
positive defined value of the dust energy density. Furthermore, the quantum
Big-Bounce is connected to the Universe turning point via a well-defined
semiclassical limit. Then we can reliably infer that the proposed scenario is
compatible with a cyclical Universe picture. We also show how, when the
contribution of the dust energy density is sufficiently high, the proposed
scenario can be extended to the Bianchi IX cosmology and therefore how it can
be regarded as a paradigm for the generic cosmological model. Finally, we
investigate the origin of the observed cut-off on the cosmological dynamics,
demonstrating how the Big-Bounce evolution can be mimicked by the same
semiclassical scenario, where the negative cosmological constant is replaced
via a polymer discretization of the Universe volume. A direct proportionality
law between such two parameters is then established.
