  In deep-inelastic processes the heavy flavor Wilson coefficients factorize
for $Q^2 \gg m^2$ into the light flavor Wilson coefficients of the
corresponding process and the massive operator matrix elements (OMEs). We
calculate the $O(\alpha_s^2)$ and $O(\alpha_s^3)$ massive OME for the flavor
non-singlet transversity distribution. At $O(\alpha_s^2)$ the OME is obtained
for general values of the Mellin variable $N$, while at $O(\alpha_s^3)$ the
moments $N = 1$ to 13 are computed. The terms $\propto T_F$ of the 3--loop
transversity anomalous dimension are obtained and results in the literature are
confirmed. We discuss the relation of these contributions to the Soffer bound
for transversity.
