plotting - How to turn off depth sorting of 3D curves for Manipulate?

Is there a way to turn off the default depth sorting of curves in a 3D output of several complicated curves ? Currently, I suspect that depth sorting has a very strong impact on performances on my Manipulate box, and would like to turn it off, to see if there's an improvement (I'm sure it will !).

Here's a cheap MWE to work with :

curve1[t_] := ParametricPlot3D[
{Sin[3 Pi s], Cos[5 Pi s^2], Cos[3 Pi s] Sin[3 Pi s]},
{s, 0.001, t},PlotStyle -> Directive[Thickness[0.02], Red]]

curve2[t_] := ParametricPlot3D[
{1.3 Sin[7 Pi s], 0.5 Cos[2 Pi s], 0.4 Sin[6 Pi s^2]},
{s, 0.001, t},PlotStyle -> Directive[Thickness[0.02], Blue]]

Manipulate[Show[

    {curve1[t], curve2[t]},
    PlotRange -> {{-1.5, 1.5}, {-1.5, 1.5}, {-1.5, 1.5}},
    Boxed -> True, Axes -> True, AxesOrigin -> {0, 0, 0},
    SphericalRegion -> True,
    Method -> {"RotationControl" -> "Globe"},
    ImageSize -> 600
    ], {{t, 1, "t"}, 0, 12, 1}]

EDIT 1 : Depth sorting is the ordering of elements in 3D space. One in front of the other, as seen by the observer. This is a standard concept in 3D modeling, games, etc... Mathematica clearly do it too (by default), if you watch closely its 3D output of thick curves. Depth sorting is necessary when there are surfaces.

In my special case, I have no surfaces, just a single complicated thin curve. I don't need depth sorting in its case. Turning off depth sorting of that curve elements should improve a lot performances.

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EDIT 2 : Here's an example of apparent no depth sorting in Mathematica, from Silvia :

Plot3D[x+y,{x,-1,1},{y,-1,1},AxesOrigin->{0,0,0},Mesh->None,Boxed->False]

While moving around that plane, you'll notice that the axis, ticks and labels are always shown "on front". They don't display any "depth sorting" of their elements. This is what I would like to achieve for curves.

There's also a strong advantage in getting no depth sorting of curves : when exporting a Mathematica 3D curve to a PDF file, and open the file with another vectorial application, you'll get the curve made of lots of small bits. The whole curve is then very hard to edit in a proper way. Without depth sorting of the curve, the curve would be of a single piece. This is highly desirable for exportation to another vectorial app.

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EDIT 3 : Compare the output from the code above, with the output from the same code with the default thickness of curves (code below). The depth sorting is still there, but it is useless since it is not visible from this output :

curve1[t_] := ParametricPlot3D[
{Sin[3 Pi s], Cos[5 Pi s^2], Cos[3 Pi s] Sin[3 Pi s]},

{s, 0.001, t},PlotStyle -> Red]

curve2[t_] := ParametricPlot3D[
{1.3 Sin[7 Pi s], 0.5 Cos[2 Pi s], 0.4 Sin[6 Pi s^2]},
{s, 0.001, t},PlotStyle -> Blue]

Manipulate[
    Show[
    {curve1[t], curve2[t]},
    PlotRange -> {{-1.5, 1.5}, {-1.5, 1.5}, {-1.5, 1.5}},

    Boxed -> True, Axes -> True, AxesOrigin -> {0, 0, 0},
    SphericalRegion -> True,
    Method -> {"RotationControl" -> "Globe"},
    ImageSize -> 600
    ], {{t, 1, "t"}, 0, 12, 1}]

Just to emphasize it : Depth sorting is not visible on thin curves and is thus useless. If a curve is very complicated, depth sorting may have a significant impact on some hardware, and it is desirable to turn it off.