NeuroEvolution of Augmenting Topologies (NEAT) is a system for evolving neural network topologies along with weights that has proven highly effective and adaptable for solving challenging reinforcement learning tasks. This paper analyses NEAT through the lens of Search Trajectory Networks (STNs), a recently proposed visual approach to study the dynamics of evolutionary algorithms. Our goal is to improve the understanding of neuroevolution systems. We present a visual and statistical analysis contrasting the behaviour of NEAT, with and without using the crossover operator, when solving the two benchmark problems outlined in the original NEAT article: XOR and double-pole balancing. Contrary to what is reported in the original NEAT article, our experiments without crossover perform significantly better in both domains.