Considerable efforts have been deployed by the European Union to create an integrated Research & Development area. In this paper, we focus on the structure and evolution of the European collaboration network as reflected by patent data. We study patent networks representing collaborations between inventors located in different geographic areas. Existing studies seem to indicate an increasing integration of the European research system, but none of them has investigated which regions contribute most to this integration. We analyze the patent coinventorship network to measure network-based distances between regions through multiple metrics, in order to evaluate the role of different areas for the integration of the EU R&D system. We study changes of the average closeness between European regions belonging to different countries. In particular, we perform a counterfactual exercise, simulating the impact on EU integration of the removal of countries and individual regions. Our findings reveal an important contribution from U.S. regions in favoring EU integration. In particular, the size and the density of the U.S. system, together with the presence of a few regional hubs, play a key role in reducing the distances between European regions.