From the Kosher Organisation site:

The word shatnes is an abbreviation of three words: Shu, Tvui, Nuz and which describe three different stages in the processing of the wool and linen fibers. Although there are differences of opinion as to exactly which processes are being referred to, most poskim maintain Shu refers to the combing of the raw fiber. is the process of spinning fibers into a thread, Tvui and Nuz refers to the twisting or weaving of the threads into cloth. The Gemorah Nida 61:2 states two opinions whether a material, in order to constitute shatnes forbidden by the Torah, requires all three of the above mentioned processes, or if only one of these processes sufficiently qualifies for a shatnes fabric. Since the Torah expresses and combines these three in the one word shatnes, we follow the opinion that a wool and linen mixture is shatnes, forbidden by the Torah, only if all three processes have been performed in the making of the material.

There is a well known disagreement between Rashi and Rabbeinu Tam with respect to these three processes. Rashi's opinion is that both the wool and linen be combined in their raw states, the two fibers are combed, spun and woven together and form a material that qualifies as shatnes forbidden by the Torah. Rabbeinu Tam disagrees and states that the requirement of , Shu, Tvui, and Nuz and is fulfilled even if the wool and linen are separately combed, spun and twisted and are later combined by weaving or attaching the two together. Thus, according to Rabbeinu Tam, the criteria for shatnes forbidden by the Torah will have been met even if they are attached by as little as two stitches as long as both the wool and linen have each undergone the process of , Shu, Tvui, and Nuz .
Did the Wool-poly blend go through the three steps?

This is why we have Kosher rabbis to tell us what is and isn't Kosher.