Possibly this is a trivial question, I'm missing something:

My experiment is based on the model

~ pos +  ring + pos:ring

the factors can take the following values:

pos = {Base,Junction,Tip} 
ring = {Down,Up,Top}

I made two DESeq2 runs, where in the first run I used the default levels of factors (as above),and in the second run I releveled the order of ring to {Up,Down,Top}. When testing the effect of "pos_Junction_vs_Base", I got 7 and 915 signifcant genes in run1 and run2, respectively. So, if my interpretation is correct then at ring=Down only 7 genes differ between Junction and Base, compared to 915 at ring=Up. If the above is correct then I expect that the interactions "posJunction.ringDown" and "posJunction.ringUp" will give about 900 signifcant genes each, to reflect the difference in Junction vs Base response between ring=Down and ring=Up. But I see only 3 signifcant genes for these interactions.

thanks a lot for any help !

There is an important difference between significant for baseline comparison X, significant for baseline comparison Y, and then testing the interaction.

One way to think about this is, suppose that the "Down" samples have a lot of noise, or there are very few of them, relative to the "Up" samples. So you have more precision to estimate the position effect for the Up samples (more significant DEGs), but less precision for estimate the effect in the Down samples. When you go to estimate the interaction, you actually need precision in both groups, in order to determine if the interaction is significant. See for example, the first two lines here: https://journals.plos.org/plosone/article?id=10.1371/journal.pone.0071079