  We consider a U(1) Gauged Linear Sigma Model (GLSM) with (2,2) supersymmetry,
leading to a susy vacua of the resolved conifold. It possesses the non-Abelian
global symmetry SU(2)xSU(2). A non-Abelian T-duality can be constructed which
can be described by gauging the global non-Abelian symmetry. This leads to a
dual action, in terms of the dual model Kaehler and superpotential terms, which
include twisted chiral superfields dependence. Comparing the effective
potentials for the U(1) fields on the original and the dual models we determine
the instanton corrections to the dual action. We obtain the supersymmetry vacua
solution of the dual model, in three cases: first in an Abelian direction
inside SU(2)xSU(2), then for an Abelian direction considering instanton
corrections and finally for a semi-chiral non Abelian vector superfield. The
dual geometry for all of these cases (SUSY vacua space) is given by T5xR.
However the instanton corrections restrict the Fayet-Iliopoulos term to be zero
and fix the theta-term, which implies that the duality is established for the
case of the singular conifold. We also discuss the U(1)A R-symmetry in the dual
model and its possible role.
