  We analyse the structure of imprecise Markov chains and study their
convergence by means of accessibility relations. We first identify the sets of
states, so-called minimal permanent classes, that are the minimal sets capable
of containing and preserving the whole probability mass of the chain. These
classes generalise the essential classes known from the classical theory. We
then define a class of extremal imprecise invariant distributions and show that
they are uniquely determined by the values of the upper probability on minimal
permanent classes. Moreover, we give conditions for unique convergence to these
extremal invariant distributions.
