Would this string work as string?
Jelly, 9 bytes
-1 byte thanks to @EriktheOutgolfer
Expect ~ instead of ‾. Returns \$0\$ or \$1\$.
O*Ɲ:⁽8ƇḂẠ

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Using this formula (but otherwise similar to the 11-byte version below):
$$n=\left\lfloor\frac{x^y}{15145}\right\rfloor$$
The transition is valid if \$n\$ is odd, or invalid if \$n\$ is even.
Commented
O*Ɲ:⁽8ƇḂẠ     - main link, taking a string          e.g. &quot;\_/&quot;
O             - get ASCII codes                     --&gt;  [92, 95, 47]
 *Ɲ           - exponentiation on all pairs         --&gt;  [92**95, 95**47]
   :⁽8Ƈ       - integer division by 15145           --&gt;  [23964828…8421, 59257069…0485]
       Ḃ      - least significant bit (i.e. parity) --&gt;  [1, 1]
        Ạ     - all values equal to 1?              --&gt;  1


Jelly,  14 12  11 bytes
Supports (and expects) the ‾ character in the input string. Returns \$0\$ or \$1\$.
O*Ɲ%276%7ỊẠ

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How?
Given two consecutive characters of ASCII codes \$x\$ and \$y\$, we want a function that checks whether they form a valid transition.
We need a non-commutative operation, because the result may change when the characters are reversed. For instance, _/ is valid but /_ is not.
Using exponentiation, a possible formula1 is:
$$n=(x^y \bmod 276)\bmod 7$$
The transition is valid if \$n\le1\$, or invalid if \$n&gt;1\$.
 chars |    x |    y | (x**y)%276 | %7 | valid
-------+------+------+------------+----+-------
   __  |   95 |   95 |      71    |  1 |  yes
   _/  |   95 |   47 |     119    |  0 |  yes
   _‾  |   95 | 8254 |     265    |  6 |   no
   _\  |   95 |   92 |     265    |  6 |   no
   /_  |   47 |   95 |      47    |  5 |   no
   //  |   47 |   47 |      47    |  5 |   no
   /‾  |   47 | 8254 |       1    |  1 |  yes
   /\  |   47 |   92 |       1    |  1 |  yes
   ‾_  | 8254 |   95 |     136    |  3 |   no
   ‾/  | 8254 |   47 |      88    |  4 |   no
   ‾‾  | 8254 | 8254 |     196    |  0 |  yes
   ‾\  | 8254 |   92 |     196    |  0 |  yes
   \_  |   92 |   95 |      92    |  1 |  yes
   \/  |   92 |   47 |      92    |  1 |  yes
   \‾  |   92 | 8254 |     184    |  2 |   no
   \\  |   92 |   92 |     184    |  2 |   no

1. Found with a brute-force search in Node.js (using BigInts)
Commented
O*Ɲ%276%7ỊẠ   - main link, taking a string          e.g. &quot;\_/&quot;
O             - get ASCII codes                     --&gt;  [92, 95, 47]
 *Ɲ           - exponentiation on all pairs         --&gt;  [92**95, 95**47]
   %276       - modulo 276                          --&gt;  [92, 119]
       %7     - modulo 7                            --&gt;  [1, 0]
         Ị    - ≤1?                                 --&gt;  [1, 1]
          Ạ   - all values equal to 1?              --&gt;  1