Unstructured pruning reduces the memory footprint in deep neural networks (DNNs). Recently, researchers proposed different types of structural pruning intending to reduce also the computation complexity. In this work, we first suggest a new measure called mask-diversity which correlates with the expected accuracy of the different types of structural pruning. We focus on the recently suggested N:M fine-grained block sparsity mask, in which for each block of M weights, we have at least N zeros. While N:M fine-grained block sparsity allows acceleration in actual modern hardware, it can be used only to accelerate the inference phase. In order to allow for similar accelerations in the training phase, we suggest a novel transposable fine-grained sparsity mask, where the same mask can be used for both forward and backward passes. Our transposable mask guarantees that both the weight matrix and its transpose follow the same sparsity pattern; thus, the matrix multiplication required for passing the error backward can also be accelerated. We formulate the problem of finding the optimal transposable-mask as a minimum-cost flow problem. Additionally, to speed up the minimum-cost flow computation, we also introduce a fast linear-time approximation that can be used when the masks dynamically change during training. Our experiments suggest a 2x speed-up in the matrix multiplications with no accuracy degradation over vision and language models. Finally, to solve the problem of switching between different structure constraints, we suggest a method to convert a pre-trained model with unstructured sparsity to an N:M fine-grained block sparsity model with little to no training. A reference implementation can be found at https://github.com/papers-submission/structuredtransposablemasks.