How to travel with a Sefer Torah from one city to another:[1]

When sending a Sefer Torah from one city to another, many are accustomed to invalidating the Sefer Torah by removing the stitching of one of the parchments, and it is then resewn in the new destination. [Practically, this is to only be done when sending the Sefer Torah through the mail system. If, however, a Jew will be escorting the Sefer Torah on its journey, such as on an airplane flight or ship, or drive by car, then the Sefer Torah is not to be unsewn.[2] In all cases, the Sefer Torah is to be well packaged with a number of coverings, and have a rain covering to protect it from getting wet. The whole Sefer Torah may be placed in a suitcase if the person will be with it the entire time. If one is taking a flight, it must be brought in as hand luggage, and remain next to the person, or on top of the person by the overhead luggage compartment, and not on the floor. It is not to be placed together with all the other luggage on the bottom of the plane. The same applies when traveling by bus. In the event that one cannot personally escort the Sefer Torah throughout the journey, and must send it through mail, or under the plane/bus, then the five Chumashim are to be unsewn and well packaged, and it may then be sent.[3]]

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[1] Chikreiy Lev Y.D. 2:6; Pesach Havdvir 135:11; Lev chaim 2:22; Kaf Hachaim 135:74; Chelkas Yaakov 1:45 [See there regarding a time of need it can be well packaged and sent through the mail and does not need to have its sewing undone]; Tzedaka Umishpat 16 footnote 9; Piskeiy Teshuvos 135:29; See Imrei Yosher 2:71 who questions this custom, as it demotes the Sefer Torah from its holiness; See Nitei Gavriel Hachnasas Sefer Torah chapter 28 for full details [although omits the idea of undoing the sewing. Vetzaruch Iyun!!

[2] See Piskeiy Teshuvos ibid; Nitei Gavriel ibid

[3] Piskeiy Teshuvos ibid; See Chelkas Yaakov 1:45 that in a time of need one can send the Sefer Torah as is, and does not need to undo the sewing, so long as it is well packaged and can be trusted to be treated properly and with care; See Nitei Gavriel ibid who omits the requirement to unsew the pages