  The main result of the present paper is the proof of the Strange Duality for
elliptic surfaces -- a duality between global sections of determinantal line
bundles on moduli spaces of stable sheaves on a fixed elliptic surface. For
this, we employ the "Marian-Oprea trick": using Bridgeland's birational
isomorphisms, we reduce the problem from a pair of general moduli spaces to a
pair of Hilbert schemes. The latter case is a theorem by Marian-Oprea.
