For texturing parametric objects like extrude and sweep and all the primitives you just type in the selection place: C1 for cap one, C2 for cap two, R1 for the the rounding, R2 …. I think this is in the user manual for sweep nurbs.
For the example you showed I would jest set up multiple Sweep Nurbs and animate them using different cap settings to kinda extrude showing the next sweep. Hope that makes sense.
/Randy