  We construct an explicit diffeomorphism between the Sasaki-Einstein spaces
Y^{p,q} and the product space S^3 \times S^2 in the cases q \le 2. When q=1 we
express the K\"ahler quotient coordinates as an SU(2) bundle over S^2 which we
trivialize. When q=2 the quotient coordinates yield a non-trivial SO(3) bundle
over S^2 with characteristic class p, which is rotated to a bundle with
characteristic class 1 and re-expressed as Y^{2,1}, reducing the problem to the
case q=1. When q>2 the fiber is a lens space which is not a Lie group, and this
construction fails. We relate the S^2 \times S^3 coordinates to those for which
the Sasaki-Einstein metric is known. We check that the RR flux on the S^3 is
normalized in accordance with Gauss' law and use this normalization to
determine the homology classes represented by the calibrated cycles. As a
by-product of our discussion we find a diffeomorphism between T^{p,q} and
Y^{p,q} spaces, which means that T^{p,q} manifolds are also topologically S^3
\times S^2.
