  Via T-duality a theory of open strings on a D1-brane wrapped along a cycle of
slanted torus is described by a U(1) gauge theory on a D2-brane in the B-field
background. It is also known that there is another dual description of the
D1-brane configuration by a non-commutative gauge theory on a D2-brane.
Therefore, these two gauge theories on D2-branes are equivalent. Recently, the
existence of a continuous set of equivalent gauge theories including these two
was suggested. We give a dual D1-brane configuration for each theory in this
set, and show that the relation among parameters for equivalent gauge theories
can be easily reproduced by rotation of the D1-brane configuration. We also
discuss a relation between this duality and Morita equivalence.
