Cerebrovascular segmentation is a crucial preliminary task for many computer-aided diagnosis tools dealing with cerebrovascular pathologies. Over the last years, deep learning based methods have been widely applied to this task. However, classic deep learning approaches struggle to capture the complex geometry and specific topology of cerebrovascular networks, which is of the utmost importance in many applications. To overcome these limitations, the clDice loss, a topological loss that focuses on the vessel centerlines, has been recently proposed. This loss requires computing the skeletons of both the manual annotation and the predicted segmentation in a differentiable way. Currently, differentiable skeletonization algorithms are either inaccurate or computationally demanding. In this article, it is proposed that a U-Net be used to compute the vascular skeleton directly from the segmentation and the magnetic resonance angiography image. This method is naturally differentiable and provides a good trade-off between accuracy and computation time. The resulting cascaded multitask U-Net is trained with the clDice loss to embed topological constraints during the segmentation. In addition to this topological guidance, this cascaded U-Net also benefits from the inductive bias generated by the skeletonization during the multitask training. This model is able to predict the cerebrovascular segmentation with a more accurate topology than current state-of-the-art methods and with a low training time. This method is evaluated on two publicly available time-of-flight magnetic resonance angiography (TOF-MRA) images datasets, also the codes of the proposed method and the reimplementation of state-of-the-art methods are made available at: https://github.com/PierreRouge/Cascaded-U-Net-for-vessel-segmentation.