The vision of NexaSphere is to create a system capable of facilitating a 3D network of networks. This framework seamlessly integrates multi-path transmission to enhance multi-connectivity in an energy-saving manner, bringing together spaceborne and airborne platforms with terrestrial infrastructure. The main goal is to deliver societal benefits to the future European landscape, with a particular focus on mobile transportation (including air mobility, railway, and automotive sectors), smart cities, and communities beyond the year 2030. NexaSphere's primary objective is to conceptualize and develop advanced hardware prototypes and software algorithms for a sustainable multi-connected 3D network. This network will integrate radio and wireless-optical technologies, and enabling network orchestration through AI-driven programmability. Additionally, NexaSphere aims to extend the edge-cloud continuum into space, creating a Radio & Wireless-Optical Connectivity Continuum from short-range to long-range. By integrating scalable simulation models in a hardware-in-the-loop approach and conducting in-lab and relevant environment validation, NexaSphere seeks to demonstrate proof-of-concept for this TN/NTN unified network architecture, targeting a Technology Readiness Level (TRL) of 4-5. These demonstrations will showcase the benefits of the proposed architecture, particularly within the mobile transportation sector, covering aeronautics, railway, and automotive industries.