  Evolution equations for leading twist operators in high orders of
perturbation theory can be restored from the spectrum of anomalous dimensions
and the calculation of the special conformal anomaly at one order less using
conformal symmetry of QCD at the Wilson-Fisher critical point at non-integer
$d=4-2\epsilon$ space-time dimensions. In this work we generalize this
technique to axial-vector operators. We calculate the corresponding three-loop
evolution kernels in Larin's scheme and derive explicit expressions for the
finite renormalization kernel that describes the difference to the vector case
to restore the conventional ${\overline{\mathrm{MS}}}$-scheme. The results are
directly applicable to deeply-virtual Compton scattering and the transition
form factor $\gamma^*\gamma\to\pi$.
