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Computing tasks are ubiquitous in space missions. Conventionally, these tasks are offloaded to ground servers for computation, where the transmission of raw data on satellite-to-ground links severely constrains the performance. To overcome this limitation, recent works offload tasks to visible low-earth-orbit (LEO) satellites. However, this offloading scheme is difficult to achieve good performance in actual networks with uneven loads because visible satellites over hotspots tend to be overloaded. Therefore, it is urgent to extend the offloading targets to the entire network. To address the network-wide offloading problem, we propose a metagraph-based computation and transmission fusion offloading scheme for multi-tier networks. Specifically, virtual edges, between the original network and its duplicate, are generated to fuse computation and transmission in single-tier networks. Then, a metagraph is employed to integrate the fusion in multi-tier networks. After assigning appropriate edge weights to the metagraph, the network-wide offloading problem can be solved by searching the shortest path. In addition, we apply the proposed scheme to solve the spatial computation offloading problem in a real multi-tier network. The superiority of the proposed scheme over two benchmark schemes are proved theoretically and empirically. Simulation results show that the proposed scheme decreases the weighted average delay by up to 87.51% and 18.70% compared with the ground offloading scheme and the visible offloading scheme, respectively.