I'm having a real hard time conceptualising the resulting surfaces of cutting a mobius strip along the boundary. I cut a 4cm Mobius strip 1cm along the boundary which resulted in interlinked 2cm Mobius Strip and a 1cm Mobius strip with double length. I realise that 3d space is not an accurate model for what is happening to the Mobius strip, can someone explain the resulting surfaces? The 2cm Mobius strip is still a Mobius strip, but what does the other strip turn into?
Additionally, how do I format it into a diagram. 
After some research I came up with the answer.
After the cut is made the model represents a mobius strip and a tube/cylinder. As the mobius strip is homeomorphic to a cylinder, the action of cutting produces a new longer strip with two full twists because the original strip only has one edge. These two full twists cause the mobius strip to become a cylinder. The centre of the strip remains a mobius strip surface.
As for the diagram, just put b and b together, then flip both arrows up. This is the diagram for a cylinder.