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Recent works on modeling the Internet topology have highlighted how the complexity of relationships between Autonomous Systems (ASes) can not be oversimplified without sacrificing accuracy in capturing route selection. Such a shortcoming can mislead the understanding, hence the prediction, of the BGP (Border Gateway Protocol) behavior. In particular, models that assume an AS to be an atomic entity fail to account for route diversity, informally defined as the selection within a single AS of multiple routes to the same destination prefix. Internet topology models are usually built out of BGP data collected by remote vantage points. Thus, in this paper we aim at extracting and characterizing the route diversity that can be measured using such dataset. Towards this goal, we devise a methodology to compute route diversity from a continuous stream of collected BGP messages. The analysis of our results shows that (i) accounting for the BGP dynamics allows to extract much more diversity than from a static snapshot of the Internet routing configuration; (ii) route diversity observed for an AS is strongly related to its location in the customer-provider hierarchy; (in) the distribution of route diversity over ASes is unlikely to be biased by the specific choice of the collection system, while the number of prefixes exhibiting route diversity can depend on both number and location of the vantage points.