Classic blue prints are indeed cyanotypes. They depend on iron ions gaining an electron from the action of light: Fe3+ + e- ==hv==> Fe2+
Fe3+ ions will not form a complex with the ferriccyanide chemical; Fe2+ ions WILL form a complex with the ferriccyanide and form a blue compound which is often called Prussian Blue. A paper was dipped in the yellow, acqueous, ferric chloride solution and then allowed to dry in the dark. This coated the paper with Fe3+ ions. Next a line drawing of a building plan, machine part, etc. was placed over the coated paper and this assembly was put into bright sunlight, or somehow exposed to ultraviolet rays. Light going through the upper drawing would strike the Fe3+ ions and these would obtain an electron from the organic material which makes up the copy paper. The electron would enter the orbital of the Fe 3+ ion converting it to Fe2+, which is slightly brown in color. Since the oxidation number of the ions is reduced from 3+ to 2+, we say the Fe 3+ ion is reduced to Fe 2+. (Silver ions are also reduced by the action of light).
Fe 3+ ions are soluble in water so they can be washed out, leaving the Fe 2+ behind. These Fe 2+ ions will complex to form Prussian Blue when the copy paper is washed with a ferriccyanide solution. Since the dark lines of the drawing prevent any light from striking the Fe 3+ ions, these line areas will remain light in color, producing a negative image. This is an inexpensive method of producing exact copies of drawings on paper, but requires liquid development.
When diazo compounds were invented it was discovered that they would turn color in strong bases. Thus if you coated a paper with a particular diazo compound and exposed it to the fumes of ammonia the paper would turn blue. Ultraviolet light prevented this reaction from happening, so exposure under a drawing and development with ammonia fumes would produce a positive.
Mimeograph depended on a paper master laid over a gel containing an aniline dye, usually blue, which was soluble in methyl alcohol. You typed on the master and the force of the typewriter letter striking the master would press the shape of the letter into the gel. An image of the letter would stick to the back of the paper master from this mechanical force, (this worked also with line drawings made with a pencil or ballpoint pen). This blue image was actually a relatively thick layer of gel containing blue dye.
To make mimeograph copies the paper master was attached to a roller about eight inches in diameter which was rotated by a crank or motor. At each revolution a blank sheet of paper was fed into a slot where a wet sponge coated the blank with a thin layer of methyl alcohol. Since the dye was only soluble in methyl alcohol (not water) as the blank paper was pressed next to the blue dye gel image, the blue dye would dissolve and transfer to the blank paper. This made a fairly good copy that smelled of alcohol for about ten minutes. Xerox wiped out the market for this process.
To be accurate, this process was not officially the "Mimeograph" process, IIRC, but was called by that name through common usage.