  Off-center stellar tidal disruption flares have been suggested to be a
powerful probe of recoiling supermassive black holes (SMBHs) out of galactic
centers due to anisotropic gravitational wave radiations. However, off-center
tidal flares can also be produced by SMBHs in merging galaxies. In this paper,
we computed the tidal flare rates by dual SMBHs in two merging galaxies before
the SMBHs become self-gravitationally bounded. We employ an analytical model to
calculate the tidal loss-cone feeding rates for both SMBHs, taking into account
two-body relaxation of stars, tidal perturbations by the companion galaxy, and
chaotic stellar orbits in triaxial gravitational potential. We show that for
typical SMBHs with mass 10^7 M_\sun, the loss-cone feeding rates are enhanced
by mergers up to \Gamma ~ 10^{-2} yr^{-1}, about two order of magnitude higher
than those by single SMBHs in isolated galaxies and about four orders of
magnitude higher than those by recoiling SMBHs. The enhancements are mainly due
to tidal perturbations by the companion galaxy. We suggest that off-center
tidal flares are overwhelmed by those from merging galaxies, making the
identification of recoiling SMBHs challenging. Based on the calculated rates,
we estimate the relative contributions of tidal flare events by single, binary,
and dual SMBH systems during cosmic time. Our calculations show that the
off-center tidal disruption flares by un-bound SMBHs in merging galaxies
contribute a fraction comparable to that by single SMBHs in isolated galaxies.
We conclude that off-center tidal disruptions are powerful tracers of the
merging history of galaxies and SMBHs.
