  The crossover among two or more types of diffusive processes represents a
vibrant theme in nonequilibrium statistical physics. In this work we propose
two models to generate crossovers among different L\'evy processes: in the
first model we change gradually the order of the derivative in the Laplacian
term of the diffusion equation, whereas in the second one we consider a
combination of fractional-derivative diffusive terms characterized by
coefficients that change in time.
  The proposals are illustrated by considering semi-analytical (i.e.,
analytical together with numerical) procedures to follow the time-dependent
solutions. We find changes between two different regimes and it is shown that,
far from the crossover regime, both models yield qualitatively similar results,
although these changes may occur in different forms for the two models. The
models introduced herein are expected to be useful for describing crossovers
among distinct diffusive regimes that occur frequently in complex systems.
