We derive both {\em local} and {\em global} generalized {\em Bianchi
identities} for classical Lagrangian field theories on gauge-natural bundles.
We show that globally defined generalized Bianchi identities can be found
without the {\em a priori} introduction of a connection. The proof is based on
a {\em global} decomposition of the {\em variational Lie derivative} of the
generalized Euler--Lagrange morphism and the representation of the
corresponding generalized Jacobi morphism on gauge-natural bundles. In
particular, we show that {\em within} a gauge-natural invariant Lagrangian
variational principle, the gauge-natural lift of infinitesimal principal
automorphism {\em is not} intrinsically arbitrary. As a consequence the
existence of {\em canonical} global superpotentials for gauge-natural Noether
conserved currents is proved without resorting to additional structures.Comment: 24 pages, minor changes, misprints corrected, a misprint in the
coordinate expression of the Jacobi morphism corrected; final version to
appear in Arch. Math. (Brno