  The set of Clifford bundles of bounded geometry over open manifolds can be
endowed with a metrizable uniform structure. For one fixed bundle $E$ we define
the generalized component $\gencomp (E)$ as the set of Clifford bundles $E'$
which have finite distance to $E$. If $D$, $D'$ are the associated generalized
Dirac operators, we prove for the pair $(D,D')$ relative index theorems, define
relative $\zeta$-- and $\eta$--functions, relative determinants and in the case
of $D=\Delta$ relative analytic torsion. To define relative $\zeta$-- and
$\eta$--functions, we assume additionally that the essential spectrum of $D^2$
has a gap above zero.
