Mirrors and Ribbons
The connect sum of a knot and its mirror is the basic example of a slice knot.
Put one above the xy-plane and mirror it below.
The mirroring sweeps out an immersed annulus.
Note how the annulus runs through itself. These self-intersections are ribbon.
Snipping along a vertical arc of the annulus leaves an immersed disk. Its boundary is the connect sum of the knot and its mirror.
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Some intersections may simply be slid away.
Others may not.
More images here.
Sketches of Topology 