Contrary to charged lepton degeneracies which are tightly constrained by the measured baryon-to-photon ratio, the allowed values of primordial neutrino asymmetries cover a large range. In order to study the evolution of these asymmetries in the early Universe, one needs to solve a set of quantum kinetic equations that include vacuum mixing effects, mean-field potentials and collisions, which represents a genuine numerical challenge. In this talk, I will present the results of a complete calculation at the epoch of neutrino decoupling, while laying emphasis on an effective description of neutrino oscillations that corresponds to averaging over the shortest time scale. In addition to reducing the computation time while preserving the accuracy of the results, this “Adiabatic Transfer of Averaged Oscillations” (ATAO) approximation provides a consistent framework to understand the origin of the so-called synchronous oscillations. This work, combined with a primordial nucleosynthesis code, provides the tools to obtain precise constraints on primordial neutrino asymmetries, thanks to the helium-4 and deuterium observed primordial abundances and the effective number of relativistic species constrained from CMB anisotropies.