The thematic topicality of the main issues of European integration through convergence, in the context subsequent to financial-inspired global recession, is relevant through both the ever more extended international impact of the inertiality of a number of integration processes, and the specific developments of convergence in the Eurozone or the European Monetary Union (EMU). The regionally structured system of the European economy, approached aggregatively from the micro-economic to the macro-economic level, like the physical system or molecularly investigated system, from economic transactions, as a major milestone, to the complexity of the transactions tissue or flows, or activities, similar to biological systems, is permanently faced with various specific disturbing factors. The European Union (EU) has historically evolved in an alternative manner, sometimes divergently or towards differentiation through separation, and sometimes convergently or coherently towards unity, fusion, integrity, evincing divergence or convergence trends, with the latter eventually becoming prevalent in the contemporary world.