So, I am asking whether 1 turquoise and 1 purple chromatid participate in crossing over or both chromatid of turquoise and purple chromatid participate on 1 to 1 basis?
The diagram you provide is just a schematic, showing a simple version to clarify what is happening in a crossover. It seems that at least once crossover has to occur in each bivalent for normal chromosome segregation to take place. This is called obligate crossover. Multiple crossovers do take place, but in eukaryotes this is usually limited to be four crossovers or less for each chromosome pair.
I think like that , different alleles coding for different traits are present on different positions on two chromatids So both can participate in the recombination only when chromatids of torquoise and purple have contrasting characters present on each chromatid Conclusion :- both chromatids of a chromosome will participate in recombination but at different time