  Dark matter haloes in cosmological filaments and walls have their spin vector
aligned (in average) with their host structure. While haloes in walls are
aligned with the plane of the wall independently of their mass, haloes in
filaments present a mass dependent two-regime orientation. Here we show that
the transition mass determining the change in the alignment regime (from
parallel to perpendicular) depends on the hierarchical level in which the halo
is located, reflecting the hierarchical nature of the Cosmic Web. By explicitly
exposing this hierarchy we are able to identify the contributions of different
components of the filament network to the spin alignment signal. We discuss a
unifying picture to describe the alignment of haloes in filaments and walls
consistent with previous results and our findings based on a two-phase angular
momentum acquisition, first via tidal torquening and later via anisotropic mass
accretion. The hierarchical identification and characterization of cosmic
structures was done with a new implementation of the Multiscale Morphology
Filter. The MMF-2 (introduced here) represents a significant improvement over
its predecessor in terms of robustness and by explicitly describing the
hierarchical relations between the elements of the Cosmic Web.
