There is no 'out of the box' capability currently. An interesting idea thought.
Currently in ArcMap you can make a selection set using the selection tool on the required AOI. You can then from Layer,Selection,AddSelectedRastersToMap have each raster added as an individual layer in a group layer. The standard tools to turn layers on/off, swipe etc can then be used.
Such capability could be added as a AddiIn relatively easily and then be customized to your exact requirements. Similarly the same can be done through any Web application. There are samples on how to work with selections and then use the LockRaster capability to display only on (or selection) of rasters.