Radiological examination of the intracranial cerebrovascular structure is crucial for pre-operative planning and post-operative follow-up. Volumetric visualization generated by computerized segmentation of the cerebrovascular structure from Time-Of-Flight Magnetic Resonance Angiography (TOF-MRA) is an appealing alternative for radiologists. This paper presents a topology-aware learning strategy with a Decorrelation Loss (DcL) for volumetric segmentation of intracranial cerebrovascular structures from multi-center MRAs. A multi-task deep CNN along with a topology-aware loss function is proposed to learn voxel-wise segmentation of the cerebrovascular tree. Domain regularization for the encoder network is achieved through Decorrelation Loss. Auxiliary tasks provide additional regularization and allow the encoder to learn higher-level intermediate representations to boost the performance of the main task. The proposed method is compared with six state-of-the-art deep learning-based 3D vessel segmentation methods. Retrospective TOF-MRA datasets with and without vascular pathologies, collected from multiple private and public data sources scanned at six different hospitals are used to perform the experiments. We have also developed an AI-assisted Graphical User Interface (GUI) based on the proposed research to assist radiologists in their daily work and establish a time-saving work process.