Crowdsensing leverages the rapid growth of sensor-embedded smartphones and human mobility for pervasive information collection. To incentivize smartphone users to participate in crowdsensing, many auction-based incentive mechanisms have been proposed for both offline and online scenarios. It has been demonstrated that the Sybil attack may undermine these mechanisms. In a Sybil attack, a user illegitimately pretends multiple identities to gain benefits. Sybil-proof incentive mechanisms have been proposed for the offline scenario. However, the problem of designing Sybil-proof online incentive mechanisms for crowdsensing is still open. Compared to the offline scenario, the online scenario provides users one more dimension of flexibility, i.e., active time, to conduct Sybil attacks, which makes this problem more challenging. In this paper, we design Sybil-proof online incentive mechanisms to deter the Sybil attack for crowdsensing. Depending on users' flexibility on performing their tasks, we investigate both single-minded and multi-minded cases and propose SOS and SOM, respectively. SOS achieves computational efficiency, individual rationality, truthfulness, and Sybil-proofness. SOM achieves individual rationality, truthfulness, and Sybil-proofness. Through extensive simulations, we evaluate the performance of SOS and SOM.