  In order to study wall crossing formula of Donaldson type invariants on the
blown-up plane, Nakajima-Yoshioka constructed a sequence of blow-up/blow-down
diagrams connecting the moduli space of torsion free framed sheaves on
projective plane, and that on its blow-up. In this paper, we prove that
Nakajima-Yoshioka's diagram realizes the minimal model program. Furthermore, we
obtain a fully-faithful embedding between the derived categories of these
moduli spaces.
