  We derive the CMB radiative transfer equation in the form of a multipole
hierarchy in the nearly-Friedmann-Robertson-Walker limit of homogeneous, but
anisotropic, universes classified via their Bianchi type. Compared with
previous calculations, this allows a more sophisticated treatment of
recombination, produces predictions for the polarization of the radiation, and
allows for reionization. Our derivation is independent of any assumptions about
the dynamical behaviour of the field equations, except that it requires
anisotropies to be small back to recombination; this is already demanded by
observations.
  We calculate the polarization signal in the Bianchi VIIh case, with the
parameters recently advocated to mimic the several large-angle anomalous
features observed in the CMB. We find that the peak polarization signal is ~
1.2 micro K for the best-fit model to the temperature anisotropies, and is
mostly confined to multipoles l<10. Remarkably, the predicted large-angle EE
and TE power spectra in the Bianchi model are consistent with WMAP observations
that are usually interpreted as evidence of early reionization. However, the
power in B-mode polarisation is predicted to be similar to the E-mode power and
parity-violating correlations are also predicted by the model; the WMAP
non-detection of either of these signals casts further strong doubts on the
veracity of attempts to explain the large-angle anomalies with global
anisotropy. On the other hand, given that there exist further dynamical degrees
of freedom in the VIIh universes that are yet to be compared with CMB
observations, we cannot at this time definitively reject the anisotropy
explanation.

Astrophysics