  A recent numerical study by A. D. Dolgov, S. H. Hansen, S. Pastor, S. T.
Petcov, G. G. Raffelt, and D. V. Semikoz (DHPPRS) [hep-ph/0201287] found that
complete or partial equilibrium between all active neutrino flavours can be
achieved before the big bang nucleosynthesis epoch via flavour oscillations, if
the oscillation parameters are those inferred from the atmospheric and solar
neutrino data, and, in some cases, if $\theta_{13}$ is also sizeable. As such,
cosmological constraints on the electron neutrino-antineutrino asymmetry are
now applicable in all three neutrino sectors. In the present work, we provide
an analytical treatment of the scenarios considered in DHPPRS, and demonstrate
that their results are stable even for very large initial asymmetries. The
equilibration mechanism can be understood in terms of an MSW-like effect for a
maximally mixed and effectively monochromatic system. We also comment on
DHPPRS's choices of mixing parameters, and their handling of collisional
effects, both of which could impinge on the extent of flavour equilibrium.
