  We calculate the two- and three-loop massive operator matrix elements (OMEs)
contributing to the heavy flavor Wilson coefficients of transversity. We obtain
the complete result for the two-loop OMEs and compute the first thirteen Mellin
moments at three-loop order. As a by-product of the calculation, the moments
N=1 to 13 of the complete two-loop and the $T_F$-part of the three-loop
transversity anomalous dimension are obtained.
