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We quantify the relative role of galaxy environment and bar presence on AGN triggering in face-on spiral galaxies using a volume-limited sample with $0.02 < z < 0.055$, $M_r < 19.5$, and $σ> 70 \rm ms s^{-1}$ selected from SDSS Data Release 7. To separate their possible entangled effects, we divide the sample into bar and non-bar sample, and each sample is further divided into three environment cases of isolated galaxies, interacting galaxies with a pair, and cluster galaxies. The isolated case is used as a control sample. For these six cases, we measure AGN fractions at a fixed central star formation rate and central velocity dispersion, $σ$. We demonstrate that the internal process of the bar-induced gas inflow is more efficient in AGN triggering than the external mechanism of the galaxy interactions in groups and cluster outskirts. The significant effects of bar instability and galaxy environments are found in galaxies with a relatively less massive bulge. We conclude that from the perspective of AGN-galaxy co-evolution, a massive black hole is one of the key drivers of spiral galaxy evolution. If it is not met, a bar instability helps the evolution, and in the absence of bars, galaxy interactions/mergers become important. In other words, in the presence of a massive central engine, the role of the two gas inflow mechanisms is reduced or almost disappears. We also find that bars in massive galaxies are very decisive in increasing AGN fractions when the host galaxies are inside clusters.