Stock exchange industry consolidation is at work since many years and has recently accelerated through competition for order flows, agreements and mergers. However, consolidation may not mean that all shocks are transmitted to every place. Therefore, following Forbes and Rigobon (2002) we distinguish convergence (as interdependence) from contagion. Long run interdependence is analyzed through overlapping rolling cointegration and shocks on correlations through multivariate GARCH models. The models are estimated on daily data from January 1 1994 and April 30 2006. We consider the DAX30, the CAC40, the FTSE100 and the NYSE indexes. We identify stock exchanges convergence between European places. However we mainly witness a leading role of the US market even after the euro area creation. Finally, dynamic correlations still exert local shocks while others are effectively transmitted.Equity market integration ; Cointegration ; Multivariate GARCH models.