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We report on the fusion of photons from two independent photonic crystal fiber sources into polarization entangled states using a fiber-based polarizing beamsplitter. We achieve fidelities of up to F = 0.74 ±0.01 with respect to the maximally entangled Bell state (φ +) using a low pump power of 5.3 mW with a success rate of 3.2 fourfold detections per second. By increasing the pump power we find that success rates of up to 111.6 fourfold detections per second can be achieved, with entanglement still present in the fused state. We characterize the fusion operation by providing a full quantum process reconstruction. Here a model is developed to describe the generation of entanglement, including the main causes of imperfection, and we show that this model fits well with the experimental results. Our work shows how non-ideal settings limit the success of the fusion, providing useful information about the practical requirements for an operation that may be used to build large entangled states in bulk and on-chip quantum photonic waveguides.