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The widespread diffusion of mobile devices integrating location capabilities makes the location of users yet another type of sensitive information used by service providers in the provision of accurate and personalized services (location-based services -- LBSs). A major problem in this context is that the privacy of users is increasingly at risk, calling for solutions balancing the benefits provided by LBSs and the privacy guarantees. In this paper, we study a novel privacy problem related to inferences of sensitive information caused by the release of consecutive positions to LBS providers. We provide an approach based on Markov chains that allows the user to continuously release her location information in a privacy-preserving way. We then define an approach to counteract different inference channels, addressing users' preferences in terms of both privacy requirements and quality of service.