Series and Parallel

series = Interpolation[{{0, {-1, 0}}, {1, {0,
      1}}, {2, {0, -1}}, {3, {1, 0}}}, InterpolationOrder -> 3];
parallel[n_] :=
  Interpolation[{{0, {-1, 0}}, {1.5, {0, n}}, {3, {1, 0}}},
   InterpolationOrder -> 2];
frame[t_] := Module[{t2},
  t2 = t - 3;
  Show[Graphics[
    {Darker@Red, PointSize[Large],
     Table[Point[{0, i}], {i, -1, 1, 1/2}]}
    , PlotRange -> 1.5],
   ParametricPlot[series[\[Tau]], {\[Tau], 0, Min[t, 3]},
    PlotStyle -> Directive[Thick, Blue]],
   If[t2 > 0,
    Table[
     ParametricPlot[parallel[n][\[Tau]], {\[Tau], 0, Min[t2, 3]},
      PlotStyle -> Directive[Thick, Orange]]
     , {n, -1, 1, 1/2}
     ]
    ,
    Graphics[{}]
    ]
   ]];
Manipulate[frame[t], {t, 0.01, 6}]