  Neutrino oscillations and mean-field effects considerably enrich the
phenomenology of neutrino evolution in the early Universe. Taking into account
these effects, most notably the neutrino self-interaction mean-field
contribution, we revisit the problem of the evolution of primordial neutrino
asymmetries including for the first time the complete expression for
collisions, which describe scattering and annihilations with
electrons/positrons and reactions among (anti)neutrinos. We show that a
generalisation of the adiabatic transfer of averaged oscillations (ATAO)
scheme, a numerical method previously developed without neutrino degeneracy and
based on the large separation of time scales in this problem, is sufficient to
reach the same accuracy as the full quantum kinetic equation integration, but
is notably faster. This approximation highlights the physics of synchronous
oscillations at play in the evolution of neutrino chemical potentials,
especially in the particular case with only two-neutrino mixing. In particular,
it allows to understand what controls the beginning and the amplitude of
oscillations, but also why there is a subsequent regime of collective
oscillations with larger frequencies. We also find that it is very important to
use the full collision term instead of relying on damping-like approximations,
in order not to overestimate how collisions reduce these synchronous
oscillations. Finally we study qualitatively how mixing parameters affect the
final neutrino configuration, and in particular we show that the CP-violating
Dirac phase cannot substantially affect the final $N_{\rm eff}$ nor the final
electronic (anti)-neutrino spectrum, and thus should not affect cosmological
observables.
