  We presented in \cite{bl2,bl7} an approach to derive the metastable behavior
of continuous-time Markov chains. We assumed in these articles that the Markov
chains visit points in the time scale in which it jumps among the metastable
sets. We replace this condition here by assumtpions on the mixing times and on
the relaxation times of the chains reflected at the boundary of the metastable
sets.
