  We investigate the axial Ward identity (AWI) for massive fermions in strong
magnetic fields. The divergence of the axial-vector current is computed at
finite temperature and/or density with the help of a relation between the
polarization and anomaly diagrams in the effective (1+1) dimensions realized in
the lowest Landau level (LLL). We discuss delicate interplay between the vacuum
and medium contributions that determines patterns of the spectral flow in the
adiabatic limit and, more generally, the diabatic chirality production rate. We
also establish an explicit relation between the AWIs from the LLL approximation
and from the familiar triangle diagrams in the naive perturbative series with
respect to the coupling constant.
