You can use the "Unsplit Lines (Data Management)" tool to merge the line segments. ArcGIS Help Link: ArcGIS Desktop
This will connect the endpoints. If the endpoints don't all link up, you may have to define the threshold in the "Environments" option.
I am also working at combining 3 separate stream layers into a single stream layer. I am required to include all 200,000 + features from the three stream layers into the final single stream layer. I will also be required to include a select few of attributes from all 3 layers to be in the final stream layer. I am also setting up a series of 'Domains' to control the data input in a few fields and finally will set up a topology to correct the many expected errors to occur as a result of the combining. A note to make worth noting is these three stream layers are not consistent with regards to placement even though they represent the same streams in most places. I'm using ArcMap 10.2.2 and have considered using the merge tool, or the update tool or append tool. I am just not sure at this point! please provide some directive, thank you!
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