Active learning has demonstrated data efficiency in many fields. Existing active learning algorithms, especially in the context of deep Bayesian active models, rely heavily on the quality of uncertainty estimations of the model. However, such uncertainty estimates could be heavily biased, especially with limited and imbalanced training data. In this paper, we propose BALanCe, a Bayesian deep active learning framework that mitigates the effect of such biases. Concretely, BALanCe employs a novel acquisition function which leverages the structure captured by equivalence hypothesis classes and facilitates differentiation among different equivalence classes. Intuitively, each equivalence class consists of instantiations of deep models with similar predictions, and BALanCe adaptively adjusts the size of the equivalence classes as learning progresses. Besides the fully sequential setting, we further propose Batch-BALanCe -- a generalization of the sequential algorithm to the batched setting -- to efficiently select batches of training examples that are jointly effective for model improvement. We show that Batch-BALanCe achieves state-of-the-art performance on several benchmark datasets for active learning, and that both algorithms can effectively handle realistic challenges that often involve multi-class and imbalanced data.