How do I cut a flap using edges or vertices Lets take a simple example of a cube.

I want to cut open one of the face of the cube from its three edges but let the third edge connected so that it looks like a flap.

In a more detailed example:

I got a airplane model 


I want to cut the cockpit windshield along the selected edges in the following photo , please I don't want to completely cut it out but to let some edges attached to main mesh
This can be done using the Rip tool. Go into edit mode, select and edge or a selection of edges (or a group of vertices):



Now press V. You will now get something like this:



For your specific instance do not select the shown edges.



Every edge is made from two vertices, one on each end. When you rip them, those vertices separate from the mesh, and a new edge is created. However the vertices at the end connect to the mesh still. In your example, pressing V would make there be a single vertex connecting the two parts, instead of two edges. Use the suggested selection to get the desire result.