AI (artificial intelligence)-based analysis of geospatial data has gained a lot of attention. Geospatial datasets are multi-dimensional; have spatiotemporal context; exist in disparate formats; and require sophisticated AI workflows that include not only the AI algorithm training and testing, but also data preprocessing and result post-processing. This complexity poses a huge challenge when it comes to full-stack AI workflow management, as researchers often use an assortment of time-intensive manual operations to manage their projects. However, none of the existing workflow management software provides a satisfying solution on hybrid resources, full file access, data flow, code control, and provenance. This paper introduces a new system named Geoweaver to improve the efficiency of full-stack AI workflow management. It supports linking all the preprocessing, AI training and testing, and post-processing steps into a single automated workflow. To demonstrate its utility, we present a use case in which Geoweaver manages end-to-end deep learning for in-time crop mapping using Landsat data. We show how Geoweaver effectively removes the tedium of managing various scripts, code, libraries, Jupyter Notebooks, datasets, servers, and platforms, greatly reducing the time, cost, and effort researchers must spend on such AI-based workflows. The concepts demonstrated through Geoweaver serve as an important building block in the future of cyberinfrastructure for AI research.