COVID-19 pandemic in Italy displayed a spatial distribution that made the tracking of its time course quite difficult. The most relevant anomaly was the marked spatial heterogeneity of COVID-19 diffusion. Lombardia region accounted for around 60% of fatal cases (while hosting 15% of Italian population). Moreover, 86% of fatalities concentrated in four Northern Italy regions. The 'explosive' outbreak of COVID-19 in Lombardia at the very beginning of pandemic fatally biased the R-like statistics routinely used to control the disease dynamics. To (at least partially) overcome this bias, we propose a new index RI = dH/dI (daily derivative ratio of H and I, given H = Healed and I = Infected), corresponding to the ratio between healed and infected patients relative daily changes. The proposed index is less flawed than R by the uncertainty related to the estimated number of infected persons and allows to follow (and possibly forecast) epidemic dynamics in a largely model-independent way. To analyze the dynamics of the epidemic, starting from the beginning of the virus spreading-when data are insufficient to make an estimate by adopting SIR model-a "sigmoidal family with delay" logistic model was introduced. That approach allowed in estimating the epidemic peak using the few data gathered even before mid-March. Based on this analysis, the peak was correctly predicted to occur by end of April. Analytical methodology of the dynamics of the epidemic we are proposing herein aims to forecast the time and intensity of the epidemic peak (forward prediction), while allowing identifying the (more likely) beginning of the epidemic (backward prediction). In addition, we established a relationship between hospitalization in intensive care units (ICU) versus deaths daily rates by avoiding the necessity to rely on precise estimates of the infected fraction of the population The joint evolution of the above parameters over time allows for a trustworthy and unbiased estimation of the dynamics of the epidemic, allowing us to clearly detect the qualitatively different character of the 'so-called' second wave with respect to the previous epidemic peak.