  In this paper, I prove that the sub-Coulomb $A(d,p)B$ reaction amplitude,
which is a solution of the three-body Faddeev equations in the
Alt-Grassberger-Sandhas (AGS) form, is peripheral if a peripheral is the
corresponding DWBA amplitude. Hence the Faddeev's reaction amplitude for the
sub-Coulomb $A(d,p)B$ reactions can also be parametrized in terms of the ANC of
the $(n\,A)$ bound state. First, I consider the original AGS equations with
separable potentials and prove that such equations are peripheral at
sub-Coulomb energies. After that, the two-particle AGS equations are derived
for the general potentials for sub-Coulomb transfer reactions. The effective
AGS potentials are expressed in terms of the DWBA amplitudes for the
sub-Coulomb reactions. Again, I demonstrate that the amplitude of the $A(d,p)B$
transfer reaction obtained from the AGS equation is peripheral and can be
parametrized in terms of the ANC for the $(nA)$ bound state because the
corresponding DWBA amplitude is peripheral. Finally, the AGS equations are
generalized by including the optical nuclear potentials in the same manner as
it is done in the DWBA. The obtained two-particle AGS equations contain the
DWBA effective potentials with distorted waves generated by the sum of the
nuclear optical and the channel Coulomb potentials. The AGS equation for the
$A(d,p)B$ reactions is analyzed above the Coulomb barrier and it is shown again
that the reaction amplitude satisfying generalized AGS equation with optical
potentials depends on the ANC if a peripheral is the DWBA amplitude. The
two-body AGS equations are generalized by including the intermediate three-body
continuum and more than one bound state in each channel.
