  In the context of the genome rearrangement problem, we analyze two well known
models, namely the reversal and the prefix reversal models, by exploiting the
connection with the notion of permutation pattern. More specifically, for any
$k$, we provide a characterization of the set of permutations having distance
$\leq k$ from the identity (which is known to be a permutation class) in terms
of what we call generating peg permutations and we describe some properties of
its basis, which allow to compute such a basis for small values of $k$.
