  It is shown that the local axial anomaly in $2-$dimensions emerges naturally
if one postulates an underlying noncommutative fuzzy structure of spacetime .
In particular the Dirac-Ginsparg-Wilson relation on ${\bf S}^2_F$ is shown to
contain an edge effect which corresponds precisely to the ``fuzzy'' $U(1)_A$
axial anomaly on the fuzzy sphere . We also derive a novel gauge-covariant
expansion of the quark propagator in the form $\frac{1}{{\cal
D}_{AF}}=\frac{a\hat{\Gamma}^L}{2}+\frac{1}{{\cal D}_{Aa}}$ where
$a=\frac{2}{2l+1}$ is the lattice spacing on ${\bf S}^2_F$, $\hat{\Gamma}^L$ is
the covariant noncommutative chirality and ${\cal D}_{Aa}$ is an effective
Dirac operator which has essentially the same IR spectrum as ${\cal D}_{AF}$
but differes from it on the UV modes. Most remarkably is the fact that both
operators share the same limit and thus the above covariant expansion is not
available in the continuum theory . The first bit in this expansion
$\frac{a\hat{\Gamma}^L}{2}$ although it vanishes as it stands in the continuum
limit, its contribution to the anomaly is exactly the canonical theta term. The
contribution of the propagator $\frac{1}{{\cal D}_{Aa}}$ is on the other hand
equal to the toplogical Chern-Simons action which in two dimensions vanishes
identically .
