  We consider the deformations of ``monomial solutions'' to Generalized
Kontsevich Model \cite{KMMMZ91a,KMMMZ91b} and establish the relation between
the flows generated by these deformations with those of $N=2$ Landau-Ginzburg
topological theories. We prove that the partition function of a generic
Generalized Kontsevich Model can be presented as a product of some
``quasiclassical'' factor and non-deformed partition function which depends
only on the sum of Miwa transformed and flat times. This result is important
for the restoration of explicit $p-q$ symmetry in the interpolation pattern
between all the $(p,q)$-minimal string models with $c<1$ and for revealing its
integrable structure in $p$-direction, determined by deformations of the
potential. It also implies the way in which supersymmetric Landau-Ginzburg
models are embedded into the general context of GKM. From the point of view of
integrable theory these deformations present a particular case of what is
called equivalent hierarchies.
