Klein Bottle 3D Animation

r = 2; \[Theta] = Pi;
Manipulate[
 GraphicsGrid[{Table[ParametricPlot3D[{
      (r + Cos[u/2] Sin[v] - Sin[u/2] Sin[2 v]) Cos[u],
      (r + Cos[u/2] Sin[v] - Sin[u/2] Sin[2 v]) Sin[u],
      Sin[u/2] Sin[v] + Cos[u/2] Sin[2 v]}, {u, 0,
      Pi + If[t > 2, If[t < 2 + Pi, (t - 2), Pi], 0]}, {v, 0,
      Pi/4 + If[t < 3 Pi/4, t,
        If[t < 2 + Pi, 3 Pi/4,
         If[t < 2 Pi + 2, 3 Pi/4 + t - 2 - Pi, 7 Pi/4]]]},
     PlotRange -> {{-4, 4}, {-4, 4}, {-2, 2}}, Boxed -> False,
     Axes -> None, PlotStyle -> Red,
     ViewPoint ->
      v], {v, {{10 Sin[\[Theta]], 10 Cos[\[Theta]],
       3}, {10 Sin[\[Theta]], 10 Cos[\[Theta]], 3}}}]}]
 , {t, 0, 2 Pi + 3}]