Through this talk I will review the principal results of my thesis. The main object of our research is the study of the exceptional divisor $E$ living in the sky $Z$ of a sequence of blow ups at smooth centers. More precisely, we are interested in recovering the sequence modulo an equivalence relation by means of the information contained in the Chow ring of the sky, $A(Z)$, and in particular by using the numerical data given by the intersection form on divisors with exceptional support $\mathcal{I}_{E,Z}$.