  We consider the problem of metastability for stochastic reversible dynamics
with exponentially small transition probabilities. We generalize previous
results in several directions. We give an estimate of the spectral gap of the
transition matrix and of the mixing time of the associated dynamics in terms of
the maximal stability level. These model-independent results hold in particular
for a large class of Probabilistic Cellular Automata (PCA), which we then focus
on. We consider the PCA in a finite volume, at small and fixed magnetic field,
and in the limit of vanishing temperature. This model is peculiar because of
the presence of three metastable states, two of which are degenerate with
respect to their energy. We identify rigorously the metastable states by giving
explicit upper bounds on the stability level of every other configuration. We
rely on these estimates to prove a recurrence property of the dynamics, which
is a cornerstone of the pathwise approach to metastability. Further, we also
identify the metastable states according to the potential-theoretic approach to
metastability, and this allows us to give precise asymptotics for the expected
transition time from any such metastable state to the stable state.
