Have a look at the help for the Integrate tool. Integrate allows you to collocate vertices based on distance. Make a backup of your data first since this tool is going to alter the original geometry of your data.
This tool may not give the results you need as it may merge lines that you do not intend to merge. Tools in ArcGIS respect selections - maybe you can improve the output from this tool by selecting only those lines from the data that you intend to integrate. For example, maybe your data are GPS tracks along roads. If those data have road names, do a select by attribute to select roads of the same name, then run integrate on the selections. To repeat this step for all your data you will need to sort out iterators in ModelBuilder, have some experience with Python and arcpy, or select manually in ArcMap and run Integrate.