Animate[Plot3D[ Evaluate[Table[Cos[x+y^2+2n],{n,3}],{x,-3,a},{y,-4,b},
  PlotStyle->Table[Opacity[0.5,Hue[i/5]],{i,5}]],Boxed->False,Axes->False,
  AspectRatio->1],{a,0,3},{b,0,4}]