Modern machine learning techniques commonly rely on complex, high-dimensional embedding representations to capture underlying structure in the data and improve performance. In order to characterize model flaws and choose a desirable representation, model builders often need to compare across multiple embedding spaces, a challenging analytical task supported by few existing tools. We first interviewed nine embedding experts in a variety of fields to characterize the diverse challenges they face and techniques they use when analyzing embedding spaces. Informed by these perspectives, we developed a novel system called Emblaze that integrates embedding space comparison within a computational notebook environment. Emblaze uses an animated, interactive scatter plot with a novel Star Trail augmentation to enable visual comparison. It also employs novel neighborhood analysis and clustering procedures to dynamically suggest groups of points with interesting changes between spaces. Through a series of case studies with ML experts, we demonstrate how interactive comparison with Emblaze can help gain new insights into embedding space structure. Emblaze is open source and available to install (see our GitHub repository for details).