We want to lift the blue curve in the annulus (shown on the left) through the covering map from the spiral strip to the annulus. First, we need to decide how to lift the initial point (shown in black on the left). All possible lifts are shown on the right. We will use the initial lift shown by the larger blue marker.

(Use the mouse wheel or arrow keys to step through.)

The solid blue part of the curve has been lifted already. We now want to lift the next short section, which is shown on the left in red. This is easy, because the short section is contained in an open set over which the covering is trivial. All possible lifts are shown on the right in red. Only one of them connects with the lifting that we have done already.

We extend our lift over the next section by using the unique possible lift that matches up with what we have already done.

We have now lifted the whole curve.