This paper exhibits a tractable and efficient way of calibrating a multiscale exponential Ornstein-Uhlenbeck stochastic volatility model including a correlation between the asset and its volatility. As opposed to many contributions where this correlation is assumed to be null, this framework allows to describe the leverage effect widely observed in equity markets. The resulting model is non exponential and driven by a degenerated noise, thus requiring high carefulness about the estimation algorithm design. The way we overcome this difficulty provides guidelines concerning the development of estimation algorithm in non standard framework. We propose to use a block-type expectation maximization algorithm along with particle smoothing. This method results in an accurate calibration process able to identify up to three time scale factors. Furthermore, we introduce an intuitive heuristic which can be used to choose the number of factors.