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