Inspired by our serendipitous discovery of six AGNs with varying broad-Halpha fluxes over years out of our searching for intermediate-mass black holes (IMBHs), we conduct a systematic investigation of changing-look (CL) and large-variability AGNs. We collect all the CL AGNs at z<0.15 and the reverberation mapped AGNs with strongly variable broad Halpha, and perform careful decomposition fittings to both their images and spectra. We find two observational facts: (1) The host galaxies of local CL and large-variability AGNs, mainly being Seyferts, are in the red (gas-poor) tail of the general Seyfert galaxy population. (2) In contrast, there is a significant trend that their more luminous counterparts namely CL and extremely variable quasars (CLQs and EVQs) are different: CLQs are generally in blue galaxies; in terms of the diagram of SFR and M* local CL Seyfert galaxies are located in the green valley, whereas CLQ hosts are in the star-forming main sequence. We propose explanations for those strongly variable Seyferts and quasars, respectively, under the thought that accretion disks broadly depend on nuclear fueling modes. Local large-variability and CL Seyferts are in nuclear famine mode, where cold-gas clumps can be formed stochastically in the fueling flow, and their episodic infall produces sharp peaks in the accretion-rate curve. CLQs and EVQs are in feast fueling mode, which may account for both their preference to blue galaxies and their variability pattern (high-amplitude tail of the continuous distribution). Lastly, we propose a new thinking: to search for IMBHs by optical variability in red galaxies.
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