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Analytic equivalence of geometric transitions

In this paper \emph{analytic equivalence} of geometric transition is defined in such a way that equivalence classes of geometric transitions turn out to be the \emph{arrows} of the \cy web. Then it seems natural and useful, both from the mathematical and physical point of view, look for privileged arrows' representatives, called \emph{canonical models}, laying the foundations of an \emph{analytic} classification of geometric transitions. At this purpose a numerical invariant, called \emph{bi--degree}, summarizing the topological, geometric and physical changing properties of a geometric transition, is defined for a large class of geometric transitions.