Mobius 3D Animation

r[\[Theta]_,
  x_, \[Alpha]_] := {-Sin[\[Theta]], Cos[\[Theta]],
   0} + {x Sin[\[Alpha]] Sin[\[Theta]], -x Cos[\[Theta]] \
Sin[\[Alpha]], x Cos[\[Alpha]]};
Manipulate[
 ParametricPlot3D[
  r[\[Theta], x,
   Pi (Tanh[\[Alpha] (\[Theta] - Pi)] + 1)/2], {\[Theta], 0,
   2 Pi}, {x, -0.5, 0.5}, Boxed -> False, Axes -> None],
 {\[Alpha], 0, 1}]