  Timing of the Crab and Vela pulsars have recently revealed very peculiar
evolutions of their spin frequency during the early stage of a glitch. We show
that these differences can be interpreted from the interactions between neutron
superfluid vortices and proton fluxoids in the core of these neutron stars. In
particular, pinning of individual vortices to fluxoids is found to have a
dramatic impact on the mutual friction between the neutron superfluid and the
rest of the star. The number of fluxoids attached to vortices turns out to be a
key parameter governing the global dynamics of the star. These results may have
implications for the interpretation of other astrophysical phenomena such as
pulsar-free precession or the r-mode instability.
