Shocks and torques produced by non-axisymmetric structures such as spiral arms and bars may transport gas to galaxy central regions. We test this hypothesis by studying the dependence of concentration of CO luminosity (C CO ), molecular gas (C mol ), and star formation rate (C SFR ) in central ∼ 2 kpc on the strength of non-axisymmetric disk structure using a sample of 57 disk galaxies selected from the EDGE-CALIFA survey. C mol is calculated using a CO-to-H 2 conversion factor that decreases with higher metallicity and higher stellar surface density. We find that C mol is systematically 0.22 dex lower than C CO . We confirm that high C mol and strong non-axisymmetric disk structure are more common in barred galaxies than in unbarred galaxies. However, we find that spiral arms also increase C mol . We show that there is a good correlation between C mol and the strength of non-axisymmetric structure (which can be due to a bar, spiral arms, or both). This suggests that the stronger the bars and spirals, the more efficient the galaxy is at transporting cold gas to its center. Despite the small subsample size, C mol of the four Seyferts are not significantly reduced compared to inactive galaxies of similar disk structure, implying that the AGN feedback in Seyferts may not notably affect the molecular gas distribution in the central ∼ 2 kpc. We find that C SFR tightly correlates with C mol in both unbarred and barred galaxies. Likewise, elevated C SFR is found in galaxies with strong disk structure. Our results suggest that the disk structure, either spirals or bars, can transport gas to the central regions, with higher inflow rates corresponding to stronger structure, and consequently boost central star formation. Both spirals and bars play, therefore, an essential role in the secular evolution of disk galaxies.