Nitrosomonas and Nitrobacter are obligate aerobic gram-negative rod bacteria. Cyanobacteria are (often facultative) anaerobic gram-negative, varied shaped bacteria. Gram negative/positive refers to the basic staining technique used for differentiation purposes when identifying bacteria. Depending on the stain retention (which is related to cell wall structure) bacteria are categorized as gram negative or gram positive. Obligate refers to if something is required; in this case for growth to happen for an obligate aerobe, oxygen must be present. Facultative organisms can make due with or without.
Cyanobacteria are some of the oldest organisms on the planet. Something had to fix nitrogen to get us the oxygen we breath, so we should be somewhat happy they want to still stick around (in our aquariums unfortunately). They use light and they use nitrogen - the end product of the nitrogen cycle which nitrobacter and nitrosomonas are a part of. Anyone that says - fix your water quality, increase your water flow, blah blah blah and it will all be better is wrong. Cyano hasn't managed to hang on for millions of years without being highly adaptable. If they have light and nitrogen, they have a food source, and they can grow.
Erythromycin is generally active against gram-positive cocci, but also to a lesser extent, gram-negative anaerobes. Erythromycin has a fairly short half-life in comparison to other antibiotics (ie. it breaks down quickly).
So what does all of this mean?
Erythromycin is usually administered to treat gram-positive infections - not to treat infections from gram-negative bugs such as the ones that inhabit our aquariums (good or bad). Since it has some impact on gram-negative anaerobes, it works against cyanobacteria. Since it is not considered effective against gram negative aerobes, the nitrobacter and nitrosomonas should not be as susceptible. Worried about creating resistance? Cyanobacteria are already resistant to antibiotics! Dosage and treatment time are likely key, but I am unfamiliar with any published research in this area (Anyone need a doctoral thesis?....).
When people talk about their tank crashing after administration of the antibiotic, my thoughts are that it is a cascading effect of the cyanobacteria die-off. The dying and stressed cyanobacteria can release cyanotoxins which can kill other organisms. When things go bad in your tank, it is probably the toxins, not the antibiotic.
So if you are going to use the antibiotic in your tank, siphon out as much of it as you can just prior to administration, this will reduce the number of cells present, and reduce the amount of potential toxins released.