Double optical feedback and double light injection are two important schemes to suppress the delay time signature peak of optical feedback chaotic lasers. In essence, the delay time signature peak is suppressed by the Mach-Zehnder interferometer. We summarize the suppression law for the delay time signature peak in the two schemes, and systematically analyze the function and mechanism of the interferometer in the suppression of the delay time signature peak. When the arms of the interferometer are close to each other, the electric field intensity and phase of the two chaotic lasers are strongly correlated. The superposition of light is dominated by coherent superposition, and the delay time signature peak of chaotic laser changes periodically with τd (delay time corresponding to the optical path difference in the interferometer). When the arms of the interferometer are obviously unequal and out of proportion, the correlation between the electric field intensity and phase of the two chaotic lasers decreases or even disappears, the superposition of light is a non-coherent superposition, but the suppression of the delay time signature peak is mainly determined by the interference term, and the main delay time signature peak does not change with τd, while generating the new delay time signature peaks.