Avoiding graphical "noise" when combining plots with Show

I use the command Show to combine plots of mathematica. For instance, the code below produces the picture below. As you can see there is some "noise" where the two curves overlap. Is there a way to avoid this? I tried playing around with Overlay, but this did not help.

point = {0, 0};
angle = Pi/4;

sur[p_List] := {p[[1]], p[[2]], p[[1]]^2 - p[[2]]^2};
cur[p_List, alpha_, s_] := sur[p + s*{Cos[alpha], Sin[alpha]}];
veloc[p_List, alpha_, s_] := D[cur[p, alpha, xi], xi] /. xi -> s;
acc[p_List, alpha_, s_] := D[veloc[p, alpha, xi], xi] /. xi -> s;
velocnorm[p_List, alpha_, s_] := veloc[p, alpha, s]/Norm[veloc[p, alpha, s]]
parx[p_List] := D[sur[{x, y}], x] /. {x -> p[[1]], y -> p[[2]]};
pary[p_List] := D[sur[{x, y}], y] /. {x -> p[[1]], y -> p[[2]]};
basex[p_List] := parx[p]/Norm[parx[p]];
basey[p_List] := (pary[p] - (pary[p].basex[p])*basex[p])/Norm[pary[p] -(pary[p].basex[p])*basex[p]];
gauss[p_List] := Cross[basex[p], basey[p]];
kappa[p_List, alpha_] := If[gauss[p].acc[p, alpha, 0] >= 0, Norm[Cross[veloc[p, alpha, 0],acc[p, alpha, 0]]]/Norm[veloc[p, alpha, 0]]^3, -Norm[Cross[veloc[p, alpha, 0], acc[p, alpha, 0]]]/Norm[veloc[p, alpha, 0]]^3];
tanvector[p_List, alpha_] := Cos[alpha]*basex[p] + Sin[alpha]*basey[p];
surface = ParametricPlot3D[sur[{x, y}], {x, -1, 1}, {y, -1, 1}, PlotStyle -> {Directive[Red, Opacity[0.8]]}, Mesh -> None];
tangentplaneplot[p_List] := ParametricPlot3D[sur[p] + u*basex[p] + v*basey[p], {u, -1, 1}, {v, -1, 1}, PlotStyle -> {White, Opacity[0.7]}, Mesh -> None];
normplaneplot[p_List, alpha_] := ParametricPlot3D[sur[p] + u*velocnorm[p, alpha, 0] + v*gauss[p], {u, -5, 5}, {v, -5,5}, PlotStyle -> {White, Opacity[0.7]}, Mesh -> None,Lighting -> "Neutral"];
curveplot[p_List, alpha_] := ParametricPlot3D[cur[p, alpha, s], {s, -1, 1}, PlotStyle -> {Blue, Thickness[0.005]}];
osccircleplot[p_List, alpha_] := If[kappa[p, alpha] == 0, ParametricPlot3D[sur[p] +zeta*velocnorm[p, alpha, 0], {zeta, -2, 2}],ParametricPlot3D[sur[p] + gauss[p]/kappa[p, alpha]+1/kappa[p, alpha]*(Cos[phi]*gauss[p] + Sin[phi]*velocnorm[p, alpha, 0]), {phi, 0, 2*Pi},PlotStyle -> {White, Thickness[0.005]}]];

xmin = -0.7;
xmax = 0.7;
ymin = -0.7;
ymax = 0.7;
zmin = -1;
zmax = 1;

Show[curveplot[point, angle], osccircleplot[point, angle],normplaneplot[point, angle],surface, Boxed -> False,PlotRange -> {{xmin, xmax}, {ymin, ymax}, {zmin, zmax}},PlotRangeClipping -> False]

Show[Graphics3D@
   First@curveplot[point, angle] /. {x_?AtomQ, y_?AtomQ, 
    z_?AtomQ} -> {x, y, z - 0.001}, osccircleplot[point, angle], 
 normplaneplot[point, angle], surface, Boxed -> False, 
 PlotRange -> {{-1, 1}, {ymin, ymax}, {zmin, zmax}}, 
 PlotRangeClipping -> True]