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Bicycle Sharing Systems (BSSs) are exponentially increasing in the urban mobility sector. They are traditionally conceived as a last-mile complement to the public transport system. In this paper, we demonstrate that BSSs can be seen as a public transport system in their own right. To do so, we build a mathematical framework for the classification of BSS trips. Using trajectory information, we create the trip index, which characterizes the intrinsic purpose of the use of BSS as transport or leisure. The construction of the trip index re