I have seen all of those methods taught. From my understanding of biology, bringing water to a boil is sufficient for most killing most pathogens. The process of heating it up to boiling, and then cooling it down, exposes the biological pathogen to high enough temperatures for long enough. If you want to be sure, do it longer, if you have the fuel. If you strain all of the suspended solids out, it will improve the effectiveness (of all purification methods).