What is the meaning of depth relation and EM in this excerpt?
EM is Electron Microscopy; the definition is found earlier in the passage in the normal form where the whole term is given followed by the abbreviation in quotes; you should look for this in the future.


  ...suited to connectomic approaches using electron microscopy (EM; Lacalli, 2009). 


I'm not super familiar with invertebrate morphology, but from context in terms of "depth relation" they are talking about inferring directions of connectivity based on their locations in EM sections. If you find axon terminals from one cell type and dendrites from another at the same depth, you can infer they are likely connected. The passage explains that this doesn't work well in invertebrates that do not have a axon -> dendrite connectivity pattern. Dendrites synapse on other dendrites, and you can't easily tell what the direction of connectivity is from EM alone.