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Gauge fixing is interpreted in BV formalism as a choice of Lagrangiansubmanifold in an odd symplectic manifold. A natural construction defines anintegration procedure on families of Lagrangian submanifolds. In stringperturbation theory, the moduli space integrals of higher genus amplitudes canbe interpreted in this way. We discuss the role of gauge symmetries in thisconstruction. We derive the conditions which should be imposed on gaugesymmetries for the consistency of our integration procedure. We explain howthese conditions behave under the deformations of the worldsheet theory. Inparticular, we show that integrated vertex operator is actually aninhomogeneous differential form on the space of Lagrangian submanifolds.

Integration over families of Lagrangian submanifolds in BV formalism