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Based on the integral field unit (IFU) data from Mapping Nearby Galaxies at Apache Point Observatory (MaNGA) survey, we develop a new method to select galaxies with biconical ionized structures, building a sample of 142 edge-on biconical ionized galaxies. We classify these 142 galaxies into 81 star-forming galaxies, 31 composite galaxies, and 30 AGNs (consisting of 23 Seyferts and 7 LI(N)ERs) according to the {\nii}-BPT diagram. The star-forming bicones have bar-like structures while AGN bicones display hourglass structures, and composite bicones exhibit transitional morphologies between them due to both black hole and star-formation activities. Star-forming bicones have intense star-formation activities in their central regions, and the primary driver of biconical structures is the central star formation rate surface density. The lack of difference in the strength of central black hole activities (traced by dust attenuation corrected {\oiii}$\lambda$5007 luminosity and Eddington ratio) between Seyfert bicones and their control samples can be naturally explained as that the accretion disk and the galactic disk are not necessarily coplanar. Additionally, the biconical galaxies with central LI(N)ER-like line ratios are edge-on disk galaxies that show strong central dust attenuation. The radial gradients of {\ha} surface brightness follow the $r^{-2.35}$ relation, roughly consistent with $r^{-2}$ profile, which is expected in the case of photoionization by a central point-like source. These observations indicate obscured AGNs or AGN echoes as the primary drivers of biconical structures in LI(N)ERs., Comment: 12 pages, 9 figures, 1 table, Accepted for publication in MNRAS