Step 1: Split the options into two groups.
Some vasculitides form granulomas on biopsy, and some do not. The question wants the one without granulomas.
Step 2: Place giant cell arteritis.
This large vessel disease of older adults shows granulomatous inflammation of the arterial wall, with giant cells attacking the internal elastic lamina. It belongs in the granulomatous group.
Step 3: Place Wegener's and Churg-Strauss.
Both are ANCA-associated vasculitides that affect small vessels, but both also produce necrotising granulomas, in the sinuses and lungs for Wegener's, and around eosinophils in Churg-Strauss. Both belong in the granulomatous group too.
Step 4: Place microscopic polyangiitis.
This is also ANCA-associated and affects small vessels like Wegener's, but biopsy shows plain necrotising vasculitis without any granuloma formation. This is what pathologists use to tell it apart from Wegener's granulomatosis.
Step 5: Conclude.
Three of the four options form granulomas. Only $microscopic\ polyangiitis$ does not.
\[ \boxed{\text{Microscopic Polyangiitis}} \]