The points of a crab have a chamber that holds sea water and a membrane that separates the blood from it by the gills. This allows neutral buoyancy.
The respiratory system consists of the gills located in the two lateral branchial chambers (Figs 1, 11, 19-36). These large chambers occupy the pointed lateral sides of the body and are bounded on all surfaces by the skeletal branchiostegite of the carapace. The branchiostegite is a double fold of body wall enclosing the branchial chamber. It is the lateral carapace. Of its two layers, the outer is heavy and calcified and part of it has been removed. The inner layer is thin, uncalcified and unsclerotized and is still intact, covering the gills. This transparent body wall lying over the gills is no more than a thin chitinous membrane investing the dorsal surface of the branchial chamber. It is almost invisible but it is all that separates the branchial chamber (which is filled with seawater) from the hemocoel (which is filled with blood).
Find and remove this thin, transparent sheet from the surface of the gills. The branchial chamber is now open and the gills are exposed for study.
Complete anatomy at http://webs.lander.edu/rsfox/invertebrates/callinectes.html