  Influence of weak uniaxial small-scale anisotropy on the stability of
inertial-range scaling regimes in a model of a passive transverse vector field
advected by an incompressible turbulent flow is investigated by means of the
field theoretic renormalization group. Weak anisotropy means that parameters
which describe anisotropy are chosen to be close to zero, therefore in all
expressions it is enough to leave only linear terms in anisotropy parameters.
Turbulent fluctuations of the velocity field are taken to have the Gaussian
statistics with zero mean and defined noise with finite correlations in time.
It is shown that stability of the inertial-range scaling regimes in the
three-dimensional case is not destroyed by anisotropy but the corresponding
stability of the two-dimensional system can be destroyed even by the presence
of weak anisotropy. A borderline dimension $d_c$ below which the stability of
the scaling regime is not present is calculated as a function of anisotropy
parameters.
