  In this paper we study certain degenerations of the mirror curves, associated
with Calabi-Yau threefolds $X_{N,M}$, and the effect of these degenerations on
the topological string partition function of $X_{N,M}$. We show that when the
mirror curve degenerates and become the union of the lower genus curves the
corresponding partition function factorizes into pieces corresponding to the
components of the degenerate mirror curve. Moreoever we show that using
degeneration of a generalised mirror curve it is possible to obtain the
partition function corresponding to $X_{N,M-1}$ from $X_{N,M}$.
