  We have started a long-term reverberation mapping project using the Wyoming
Infrared Observatory 2.3 meter telescope titled "Monitoring AGNs with H\beta\
Asymmetry" (MAHA). The motivations of the project are to explore the geometry
and kinematics of the gas responsible for complex H\beta\ emission-line
profiles, ideally leading to an understanding of the structures and origins of
the broad-line region (BLR). Furthermore, such a project provides the
opportunity to search for evidence of close binary supermassive black holes. We
describe MAHA and report initial results from our first campaign, from December
2016 to May 2017, highlighting velocity-resolved time lags for four AGNs with
asymmetric H\beta\ lines. We find that 3C 120, Ark 120, and Mrk 6 display
complex features different from the simple signatures expected for pure
outflow, inflow, or a Keplerian disk. While three of the objects have been
previously reverberation mapped, including velocity-resolved time lags in the
cases of 3C 120 and Mrk 6, we report a time lag and corresponding black hole
mass measurement for SBS 1518+593 for the first time. Furthermore, SBS
1518+593, the least asymmetric of the four, does show velocity-resolved time
lags characteristic of a Keplerian disk or virialized motion more generally.
Also, the velocity-resolved time lags of 3C 120 have significantly changed
since previously observed, indicating an evolution of its BLR structure. Future
analyses of the data for these objects and others in MAHA will explore the full
diversity of H\beta\ lines and the physics of AGN BLRs.
