Sleep plays a vital role in human health, both mental and physical. Sleep disorders like sleep apnea are increasing in prevalence, with the rapid increase in factors like obesity. Sleep apnea is most commonly treated with Continuous Positive Air Pressure (CPAP) therapy. Presently, however, there is no mechanism to monitor a patient's progress with CPAP. Accurate detection of sleep stages from CPAP flow signal is crucial for such a mechanism. We propose, for the first time, an automated sleep staging model based only on the flow signal. Deep neural networks have recently shown high accuracy on sleep staging by eliminating handcrafted features. However, these methods focus exclusively on extracting informative features from the input signal, without paying much attention to the dynamics of sleep stages in the output sequence. We propose an end-to-end framework that uses a combination of deep convolution and recurrent neural networks to extract high-level features from raw flow signal with a structured output layer based on a conditional random field to model the temporal transition structure of the sleep stages. We improve upon the previous methods by 10% using our model, that can be augmented to the previous sleep staging deep learning methods. We also show that our method can be used to accurately track sleep metrics like sleep efficiency calculated from sleep stages that can be deployed for monitoring the response of CPAP therapy on sleep apnea patients. Apart from the technical contributions, we expect this study to motivate new research questions in sleep science.