  We discuss aspects of the theory of non-invertible transformations which
enter in the problem of classification of diffe\-ren\-tial-difference equations
and, in particular, the notion of Miura type transformation. We introduce the
concept of non--Miura type linearizable transformation and we present
techniques which allow one to construct simple linearizable transformations and
help us to solve the classification problem. This theory is illustrated by the
example of a new integrable differential--difference equation depending on 5
lattice points, interesting from the viewpoint of the non-invertible
transformation which relate it to an Itoh--Narita--Bogoyavlensky equation.
