Airy beams have three major properties: non-diffraction, self-acceleration, and self-healing, among which the self-acceleration property is the most attractive. To fully understand the Airy beam's self-acceleration characteristics and to ensure its trajectory's integrity, the relative position and rotation angle of the cubic phase in the phase diagram was changed based on geometric transformation to explore the transmission characteristics of the Airy beam. Fourier optics was used to derive the corresponding spectral formula. The results show that the phase map geometric transformation modulation can significantly change the position of the propagation trajectory and the spatial deflection of the Airy beam. This study provides a more comprehensive understanding of the field and application of the self-accelerating properties of Airy beams and provides new ideas for the understanding of controlling other accelerated beams.