  The key result in the present paper is a direct analogue of the celebrated
Thurston's Theorem for marked Thurston maps with parabolic orbifolds. Combining
this result with previously developed techniques, we prove that every Thurston
map can be constructively geometrized in a canonical fashion. As a consequence,
we give a partial resolution of the general problem of decidability of Thurston
equivalence of two postcritically finite branched covers of the two-sphere.
