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how to plot 'carpet' of curves

I have a time series of curves {f1(x),f2(x),... } associated with times 
{t1,t2,...}. I want to plot the curves 'cascaded':  curve f1 at plane 
t=t1, f2 at plane t=t2, etc. Using lists {f,x,t} I am able to use 
ListPlot3D and it pretty much shows what I want but still it is not a 
'carpet' of curves. I guess I could make ListPlot3D to behave like 
ParametricPlot3D  but was not able to figure out how. Any help is highly 

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