  Pulsar glitches are attributed to the sudden re-coupling of very weakly
coupled large scale superfluid components in the neutron star interior. This
process leads to rapid exchange of angular momentum and an increase in spin
frequency. The transfer of angular momentum is regulated by a dissipative
mutual friction, whose strength defines the spin-up timescale of a glitch.
Hence, observations of glitch rises can be used to shed light on the dominant
microphysical interactions at work in the high density interior of the star. We
present a simple analytical model, complemented with more detailed numerical
simulations, which produces a fast spin-up followed by a more gradual rise.
Such features are observed in some large glitches of the Crab pulsar, including
the largest recent glitch of 2017. We also use observations to constrain the
mutual friction coefficient of the glitch-driving region for two possible
locations: the inner crust and outer core of the star. We find that the
features of Crab glitches require smaller values of the mutual friction
coefficient than those needed to explain the much faster Vela spin-ups. This
suggests a crustal origin for the former but an outer core contribution for the
latter.
