New answers tagged 4-manifolds
The answer is yes. You can embed U and V disjointly in $S^4$, and then do the connected sum at infinity, or `end-connected sum', using an arc going from one to the other. This construction is, I guess, what you intend by $U \cup V$, and is discussed for example in Gompf's paper, Three exotic R4's and other anomalies, J. Differential Geom. 18 (1983), no. 2, ...
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