Water filters will only remove bacteria and in some cases viruses from the water. The toxins released by cyanobacteria are much smaller and like most small molecules will not be removed by the filters. So if all the toxin is still in the algae, you will be safe as the filter can remove the algae and the toxin load it carries. If the toxins have left the algae and are dissolved in the water, you might regret it.
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