Relation between red filter band and redshift? I am interested in knowing what is the significance of red filter band  in the study of redshift dependence of spatial orientation of galaxies?
 A: If I understand your question right, you want to know what is so special about the red and infrared bands / filters in studying the spatial distribution of galaxies.
It is true that the red and IR bands are used inreasingly much in the mapping of galaxies at high $z$. This is because at these redshifts, we often use the Lyman-Alpha line to both detect and determine redshifts of the galaxies we find. The Lyman-Alpha line has a rest wavelength of 1216Å, and it is quite special in that 2/3 of all photons capable of ionizing hydrogen emitted by the young stars in a galaxy will recombine and be re-emitted as Lyman-Alpha. This means that this line is often the strongest, often even the only feature that we can see at high redshifts.
At a redshifte of 4, the wavelength of the Ly$\alpha$ line is $1216 Å \cdot (1+4) = 6080Å$, so beyond this redshift, the $Ly\alpha$ line enters the red bands.
Besides, due to the strong absorption of ionizing photons, anything with a rest wavelength of less than 918Å is simply not present. This limit will enter the red bands at redshifts 5-6. Anything interesting will happen to the red side - and mostly, quite far to the red side -  of this limit, which is reflected in the increasing interest in IR telescope like e.g. the James Webb Space Telescope these years.
