  Degeneracies among parameters of the cosmological model are known to
drastically limit the information contained in the matter distribution. In the
first paper of this series, we shown that the cosmic web environments; namely
the voids, walls, filaments and nodes; can be used as a leverage to improve the
real-space constraints on a set of six cosmological parameters, including the
summed neutrino mass.
  Following-upon these results, we propose to study the achievable constraints
of environment-dependent power spectra in redshift space where the velocities
add up information to the standard two-point statistics by breaking the
isotropy of the matter density field. A Fisher analysis based on a set of
thousands of Quijote simulations allows us to conclude that the combination of
power spectra computed in the several cosmic web environments is able to break
some degeneracies. Compared to the matter monopole and quadrupole information
alone, the combination of environment-dependent spectra tightens down the
constraints on key parameters like the matter density or the summed neutrino
mass by up to a factor of $5.5$. Additionally, while the information contained
in the matter statistic quickly saturates at mildly non-linear scales in
redshift space, the combination of power spectra in the environments appears as
a goldmine of information able to improve the constraints at all the studied
scales from $0.1$ to $0.5$ $h$/Mpc and suggests that further improvements are
reachable at even finer scales.
