  We examine several classes of manifolds which have the same cohomology ring
as an Eschenburg space (a family of biquotients which is a main source of
manifolds with positive curvature). One family are the 3-sphere bundles over
CP^2. Another are the circle bundles over a base, which itself is one of the
family of CP^1 bundles over CP^2. We classify such manifolds up to
diffeomorphism using the Kreck-Stolz invariants. Comparisons of the invariants
is then used to find many diffeomorphism of the total space of these bundles
with positively curved Eschenburg spaces. The total space of each bundle (in
the case where the bundle is not spin) also admit a metric with non-negative
sectional curvature, and in some cases an Einstein metric as well.
