  In these notes evidence is presented for intepreting the moduli space of the
integrable model associated to $N\!=\!2$ gauge theories with $N\!=\!4$ matter
content, in terms of Calabi-Yau manifolds. We restrict to the case of gauge
group $SU(2)$, which is compared with the moduli space of the Calabi-Yau
manifold $WP_{11226}^{12}$ appearing in the rank three dual pair $(K^{3}\times
T^{2} / WP_{11226}^{12})$. The singularity loci of both spaces are maped in a
one to one way and, in the weak coupling limit, $N\!=\!2$ $SU(2)$ pure
Yang-Mills is obtained in both cases by the same type of blow up. Comments on
the interpretation of the strong coupling locus from the perspective of the
integrable system are done.
