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Is it possible to find a specific example of two fiber bundles with the same base, group, fiber and homeomorphic total spaces but these bundles are not equivalent/isomorphic, if so

should I find a bundle map F between two bundles, inducing identity on the common base but F does not preserve fibers? (I don't know what it means, got mixed up) or

should I define the action of group on fibers differently?

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    for each (h,j) in Z+Z there corresponds an S^3 bundle over S^4 and when h+j=1 the total spaces are all homeomorphic to S^7 and the group is SO(4). I try to understand where the difference come from?2012-06-29
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    Why do you ask wether such bundles exist if you already know examples of this behavior?2012-06-29

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