  In a recent article of Kenny De Commer, was investigated a Morita equivalence
between locally compact quantum groups, in which a measured quantum groupoid,
of basis $\mathbb{C}^2$, was constructed as a linking object. Here, we
generalize all these constructions and concepts to the level of measured
quantum groupoids. As for locally compact quantum groups, we apply this
construction to the deformation of a measured quantum groupoid by a 2-cocycle.
