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We identify and phase a sample of 107 Cepheids with 10<P/days<100 in M81using the LBT and calibrate their BVI mean magnitudes with archival HST data.The use of a ground-based telescope to identify and phase the Cepheids and HSTonly for the final calibration reduces the demand on HST by nearly an order ofmagnitude and yields Period-Luminosity (PL) relations with dispersionscomparable to the best LMC samples. We fit the sample using the OGLE-II LMC PLrelations and are unable to find a self-consistent distance for different bandcombinations or radial locations within M81. We can do so after adding a radialdependence to the PL zero point that corresponds to a luminosity dependence onmetallicity of g_mu=-0.56+/-0.36 mag/dex. We find marginal evidence for a shiftin color as a function of metallicity, distinguishable from the effects ofextinction, of g_2=+0.07+/-0.03 mag/dex. We find a distance modulus for M81,relative to the LMC, of mu(M81-LMC)=9.39+/-0.14 mag, including uncertaintiesdue to the metallicity corrections. This corresponds to a distance to M81 of3.6+/-0.2 Mpc, assuming a LMC distance modulus of 18.41 mag. We carry out ajoint analysis of M81 and NGC4258 Cepheids and simultaneously solve for thedistance of M81 relative to NGC4258 and the metallicity corrections. Given thecurrent data, the uncertainties of such joint fits are dominated by therelative metallicities and the abundance gradients rather than by measurementerrors of the Cepheid magnitudes or colors. We find mu(M81-LMC)=9.40(-0.11/+0.15) mag, mu(N4258-LMC)=11.08 (-0.17/+0.21) mag andmu(N4258-M81)=1.68+/-0.08 mag and joint metallicity corrections of g_mu=-0.62(-0.35/+0.31) mag/dex and g_2=0.01+/-0.01 mag/dex. Quantitative analyses ofCepheid distances must take into account both the metallicity dependencies ofthe Cepheids and the uncertainties in the abundance estimates. (ABRIDGED)

A Study of Cepheids in M81 with the Large Binocular Telescope (Efficiently Calibrated with HST)