A promise of economic convergence was one of the core reasons behind the creation of the Euro. At no time in the Euro area history has this promise been more important than in the years following the series of the 2008-2013 crises, primarily because the crisis has significantly adversely impacted not only the 'new member states' (who may or may not have been on the 'convergence path' prior to the crisis onset), but also the 'old member states' (who were supposed to have been on the convergence path prior to the crisis). The latter group of states is the so-called Euro periphery: Greece, Italy, Spain and Portugal.
So have the Euro delivered convergence for these states since the end of the Euro area crises, starting with 2014? The answer is firmly 'No'.
In simple terms, the idea that the common currency has been delivering on its core promise of facilitating economic convergence between the rich Euro area states and the less prosperous ones holds no water.