We discuss singularity analysis and bilinear integrability of four Bogoyavlensky differential-difference equations. Three of them are completely integrable and the fourth is, to our knowledge, a new one. Blending the singularity confinement with Painlevé property reveals strictly confining and anticonfining (weakly confining) singularity pat- terns. The strictly confining patterns are useful because they provide different representations using tau functions and a possible extension of the so called "express method" for testing integrability. For the new proposed equation we get also the bilinear form and multisoliton solution, being a good candidate for a new integrable system. In addition, using bilinear formalism we recover the integrable time-discretisations of the first three systems.