We present a readily accessible web-based interactive system for ray casting-based flow visualization in quotient spaces and ${\mathbb{S}^3}$. It is the result of a long-term close collaboration with researchers from symplectic geometry, and focuses on accessibility, flexibility, and provenance. By storing its state in URLs and providing a version-aware mechanism to link from images in PDFs to the online tool in the state that produced the image, we ensure reproducibility, explorability, and collaboration. We exemplify the utility of our approach with examples from mathematics and symplectic geometry.