  We provide concrete models for generalized morphisms and Morita equivalences
of topological 2-groupoids by introducing the notions of crossings and crossed
extensions of groupoid crossed modules. A systematic study of these objects is
elaborated and an explicit description of how they do yield a groupoid and
geometric picture of weak 2-groupoid morphisms is presented. Specifically, we
construct a weak 3-category whose objects are crossed modules of topological
groupoids and in which weak 1-isomorphisms correspond to Morita equivalences in
the "category" of topological 2-groupoids.
