I´m looking for information about the intersection of two vector bundles (principally trivial bundles, but no necessarily). I´m trying to make a picture (literally) of reflexive finite generated modules.


  

Another related topic is sub-budles of a vector bundles.


  

All suggestions are wellcome!




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**Edit**: I try to be more specific.


Suppose two sub-bundles of a bundle over a topological space X. We can do the intersection of their vector fibers in each point of base space and collect this intersection vector fibers along the base space. Then we can give it a topology, restriction of the bigger vector bundle. 


What´s about of this "submodule of sections"? 


Is it another vector bundle? 


Has another interesting structure?



About the intersection of two vector bundles
You need to refine the question to get better answers, but here are some thoughts:


1) Over a normal variety, you can think of line bundles as divisors, and "intersect" them.


2) A vector bundle can be represented by a reflexive sheaf, but being reflexive is a lot weaker. 


