We present a general framework that allows to construct systematically analytic calculi for a large family of (propositional) many-valued logics --- called projective logics --- characterized by a special format of their semantics. All finite-valued logics as well as infinite-valued Godel logic are projective. As a case-study, sequent of relations calculi for Godel logics are derived. A comparison with some other analytic calculi is provided