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The purpose of this paper is to explain and to generalize, in a homotopicalway, the result of Barannikov-Kontsevich and Manin which states that theunderlying homology groups of some Batalin-Vilkovisky algebras carry aFrobenius manifold structure. To this extent, we first make the minimal modelfor the operad encoding BV-algebras explicit. Then we prove a homotopy transfertheorem for the associated notion of homotopy BV-algebra. The final resultprovides an extension of the action of the homology of theDeligne-Mumford-Knudsen moduli space of genus 0 curves on the homology of someBV-algebras to an action via higher homotopical operations organized by thecohomology of the open moduli space of genus zero curves. Applications inPoisson geometry and Lie algebra cohomology and to the Mirror Symmetryconjecture are given.

The minimal model for the Batalin-Vilkovisky operad