  In this paper we study in detail the equivalence of the recently introduced
Born-Infeld self dual model to the Abelian Born-Infeld-Chern-Simons model in
2+1 dimensions. We first apply the improved Batalin, Fradkin and Tyutin scheme,
to embed the Born-Infeld Self dual model to a gauge system and show that the
embedded model is equivalent to Abelian Born-Infeld-Chern-Simons theory. Next,
using Buscher's duality procedure, we demonstrate this equivalence in a
covariant Lagrangian formulation and also derive the mapping between the
n-point correlators of the (dual) field strength in Born-Infeld Chern-Simons
theory and of basic field in Born-Infeld Self dual model. Using this
equivalence, the bosonization of a massive Dirac theory with a non-polynomial
Thirring type current-current coupling, to leading order in (inverse) fermion
mass is also discussed. We also re-derive it using a master Lagrangian.
Finally, the operator equivalence between the fermionic current and (dual)
field strength of Born-Infeld Chern-Simons theory is deduced at the level of
correlators and using this the current-current commutators are obtained.
