  This paper is aimed at investigating links between Fell bundles over Morita
equivalent groupoids and their corresponding reduced C*-algebras. Mainly, we
review the notion of Fell pairs over a Morita equivalence of groupoids, and
give the analogue of the Renault's Equivalence Theorem for the reduced
C*-algebras of equivalent Fell systems. Eventually, we will use this theorem to
connect the reduced C*-algebra of an S^1-central groupoid extension to that of
its associated Dixmier-Douady bundle.
