  A powerful result in theoretical cosmology states that a subset of
anisotropic Bianchi models can be seen as the homogeneous limit of (standard)
linear cosmological perturbations. Such models are precisely those leading to
Friedmann spacetimes in the limit of zero anisotropy. Building on previous
works, we give a comprehensive exposition of this result, and perform the
detailed identification between anisotropic degrees of freedom and their
corresponding scalar, vector, and tensor perturbations of standard perturbation
theory. In particular, we find that anisotropic models very close to open
(i.e., negatively curved) Friedmann spaces correspond to some type of
super-curvature perturbations. As a consequence, provided anisotropy is mild,
its effects on all types of cosmological observables can always be computed as
simple extensions of the standard techniques used in relativistic perturbation
theory around Friedmann models. This fact opens the possibility to consistently
constrain, for all cosmological observables, the presence of large scale
anisotropies on the top of the stochastic fluctuations.
