  The limiting transitions between different types of quantizations are studied
by the deformation theory methods. We prove that for the first order coboundary
deformation (g,g*_1 + x g*_2) of a Lie bialgebra (g,g*) one can always get the
quantized Lie bialgebra (g,g*_2) as a limit of the sequence of quantizations of
the type A(g,g*_1). The obtained results are illustrated by some
low-dimensional examples of quantized Lie algebras and superalgebras.
