Save as Prefab
By default, the modified mesh is serialized in the scene file. (the xxx.unity file)
In this form, you could not access it in other scenes or save it as prefab.
You could save the mesh as prefab with the method below, so you can access it in other scenes.
Click the "Prefab" button on the GUI, it will prompt you to select a location to save the prefab.
Be noted that, if you've already done that before, then you don't have to do it again to make prefab, just drag it into project window will do.
In another word, it will not create two mesh asset for one object.