Simplify triple integral over time differences

Question

I know that if I have the following integral \begin{equation} \int_{-\infty}^t dt_1 e^{-|t-t_1|} f(t-t_1) \end{equation} by defining a new variable $\tau=t-t_1$, it can be transformed into \begin{equation} \int_0^\infty d\tau e^{-\tau} f(\tau) \end{equation} which makes the integration much easier by removing the absolute value. I am now trying the same trick with a much-involved triple integral \begin{equation} \int_{-\infty}^t dt_1 \int_{-\infty}^{t_1} dt_2 \int_{-\infty}^{t_2} dt_3 (e^{-|t-t_1|}e^{-|t_2-t_3|}+e^{-|t-t_3|}e^{-|t_2-t_1|}) f(t-t_1)g(t_1-t_2)h(t_2-t_3)l(t_3-t) \end{equation} The problem is that now if I define $\tau=t-t_1$, it will appear in the upper integration of the second integral. Is there any way to circumvent this?