  We study the geometric phase transitions that accompany the dynamic
rearrangement of vacuum under spontaneous violation of initial gauge symmetry.
The rearrangement may give rise to condensates of three types, namely the
scalar, axially symmetric, and entirely anisotropic condensates. The flat
space-time keeps being the Minkowski space in the only case of scalar
condensate. The anisotropic condensate having arisen, the respective anisotropy
occurs also in space-time. In this case the space-time filled with axially
symmetric condensate proves to be a flat relativistically invariant Finslerian
space with partially broken 3D isotropy, while the space-time filled with
entirely anisotropic condensate proves to be a flat relativistically invariant
Finslerian space with entirely broken 3D isotropy. The two Finslerian space
types are described briefly in the extended introduction to the work, while the
original part of the latter is devoted to determining observable 3-velocities
in the entirely anisotropic Finslerian event space. The main difficulties that
are overcome in solving that problem arose from the nonstandard form of the
light cone equation and from the necessity of correct introducing of a norm in
the linear vector space of rapidities.
