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A construction of conservation laws and conserved quantities forperturbations in arbitrary metric theories of gravity is developed. In anarbitrary field theory, with the use of incorporating an auxiliary metric intothe initial Lagrangian covariantized Noether identities are carried out.Identically conserved currents with corresponding superpotentials are unitedinto a family. Such a generalized formalism of the covariantized identitiesgives a natural basis for constructing conserved quantities for perturbations.A new family of conserved currents and correspondent superpotentials forperturbations on arbitrary curved backgrounds in metric theories is suggested.The conserved quantities are both of pure canonical Noether and of Belinfantecorrected types. To test the results each of the superpotentials of the familyis applied to calculate the mass of the Schwarzschild-anti-de Sitter black holein the Einstein-Gauss-Bonnet gravity. Using all the superpotentials of thefamily gives the standard accepted mass.

Covariantized Noether identities and conservation laws for perturbations in metric theories of gravity